I'm just going to connect some dots, because I'm a bit OCD like that and because just leaving that quote hanging is a little rude...
Miriam-Webster wrote:invoke
verb in·voke \in-ˈvōk\
1
a : to petition for help or support
b : to appeal to or cite as authority
2
: to call forth by incantation : conjure
3
: to make an earnest request for : solicit
4
: to put into effect or operation : implement
5
: bring about, cause
In the earlier quote, it is 2nd definition that applies, which has a verbal component.
The context of that quote is that one's recitation/invocation is useless if one has no mental movement behind the recitation/invocation.
If one does not understand what one is reciting/invoking, then one is merely performing an action with the mouth.
Buddha Name Recitation:
Chinese: 念佛, pinyin: niànfó;
Japanese: 念仏 nembutsu;
Korean: 염불 yeombul;
Vietnamese: niệm Phật
Sanscrit: buddhānusmṛti
All of which mean "mindfulness of the Buddha."
Now your entire straw man rests on this fictional idea that there is a Buddha Recitation that does not involve thinking of that Buddha and the associated narrative. To tell the truth, given the number of quotes I've given to the contrary, it would be up to you to provide any substantial evidence of such a fiction.
The clearest statement I can give regarding burden proof to refute my case is this:
if an understanding is not at all required for Nembutsu/Nianfo (mindfulness of the Buddha) Recitation, then show me a Pure Land tradition that does not give Dharma talks, show me a tradition that does not recommend reading the sutras, show me a tradition where one is given status of a teacher just because they know the syllables to pronounce the name, show me an actual Pure Land tradition that says not to even think of the Buddha when reciting.
Now I doubt you're going to find a single existence of such a school, let alone among the Chinese schools.
But I'll help you by ruling out some candidates.
Let's start with most radical interpretation and bring it back...
Ippen wrote:"The six mystic characters (na-mu-a-mi-da-butsu) represent the universal absolute Dharma, and all things human and material are nothing but absolute reality. All action free from affliction is the realization of that absolute reality. The person who comes to know this is most excellent.”
I was mistaken before. This is the realization that Ippen received. His earlier statement that I quoted before was given to Hoto Kokushi (aka Kakushin),
a Fuke Shu Zen master, so no - as an itinerant hijiri, the
Inka given to Ippen by Kakushin was not insignificant. Ippen taught recitation with absolute surrender, that even common faith was useless when it came from a deluded mind. This surrender is consistent with Vasubandhu, who said the singleness of mind (shamatha) comes from the intense wish to see Amida Buddha. This clearly shows some level of mental movement.
Shinran wrote:Shinran in his teaching emphasized more greatly faith and the all-encompassing other-power (tariki) of Amida. So in certain ways, his teaching has some similarities with Kosai’s “single calling” teaching. Even though Shinran had no objection to any number of recitations, he did emphasize an absolute value in one. He felt that one recitation best expressed the way of salvation which Amida chose as the easiest possible for all persons. From the standpoint of faith, the “single calling” coincides with the moment in which faith arises in the mind and also expresses the deep joy of that faith in Amida Buddha’s wonderful compassion. In such a deeply believing recitation, there is enough karmic merit to bring the person to Birth in the Pure Land. From the time that a person attains this faith, his or her nembutsu repetitions are all prompted by a joyous gratitude toward Amida Buddha for the compassion that has now saved them - they are no longer calls for salvation. The power to bring about this emancipating faith is not on the part of the person but is Amida’s gift. And so one simply focuses on giving deep praise to this compassionate and emancipating power of Amida, while leaving behind all other practices. As a person already fully embraced by Amida, one should go through life expressing this by following basic morality and ethics, and fulfilling one’s duties to family, community and the larger society. Thus, to make a broad generalization, the nembutsu of Honen and the Jodo school represents more the process of establishing of a deep relationship with Amida Buddha, while the nembutsu of Shinran and the Jodo Shin school represents a recognition of that ever present relationship to Amida’s grace. In this way, the Pure Land for Jodo school believers is more of an existential place one goes to after death through establishing a firm relationship with Amida, while the Pure Land for Jodo Shin followers is none other than this world when it is illuminated by Amida’s power. Together, these two notions of nembutsu and Pure Land compliment each other by providing a means to confront both life and death.
The above isn't even written by a Shin school, but it's a beautiful display of how narrative drives recitation/invocation. There's another quote on that link from Shinran himself (from his Lamp for the Latter Ages) that is in the same vein (probably does a better job of stressing the importance of the 1st & 2nd of the 3 minds), but I think this one sums it up nicely. The above paragraph lines up rather well with Bodhidharma's quote even. You still have to know who Amida is, a general idea of what a Buddha is, what emancipation/liberation/salvation is, what compassion is, what the Pure Land is, and why you need all that stuff for any of that to even work. To assert otherwise is just being foolish.
Honen wrote:"In China and Japan, many Buddhist masters and scholars understand that the nembutsu is to meditate deeply on Amida Buddha and the Pure Land. However, I do not understand the nembutsu in this way. Reciting the nembutsu does not come from studying and understanding its meaning. There is no other reason or cause by which we can utterly believe in attaining birth in the Pure Land than the nembutsu itself. Reciting the nembutsu and believing in birth in the Pure Land naturally gives rise to the three minds (sanjin) and the four modes of practice (shishu). If I am withholding any deeper knowledge beyond simple recitation of the nembutsu, then may I lose sight of the compassion of Shakyamuni and Amida Buddha and slip through the embrace of Amida's original vow. Even if those who believe in the nembutsu study the teaching which Shakyamuni taught his whole life, they should not put on any airs and should sincerely practice the nembutsu, just as an illiterate fool, a nun or one who is ignorant of Buddhism. I hereby authorize this document with my hand print. The Jodo Shu way of the established mind (anjin) is completely imparted here. I, Genku, have no other teaching than this. In order to prevent misinterpretation after my passing away, I make this final testament." January 23, the Second Year of Kenryaku (1212)
"meditate deeply" = he's referring to the harsh 90 day practice of the Pratyutpanna Samadhi Sutra that requires absolutely no outside thoughts, extremely strict discipline, and 3 months of no sleep while performing walking recitation meditation. This practice was paired down to 7 days on Mt Hiei, but was still beyond the scope of most people. He's also rejecting the idea of exclusively doing visualization exercises on the images described in the Visualization Sutra. Knowledge of the adornments of the Pure Lands come through reading the sutras, he said that combined with thinking of Amida and wishing to be in that land as one recites were enough to see those visualizations (as was pointed out in early quotes from the Senchakushu).
"Reciting the nembutsu does not come from studying and understanding its meaning" = he's saying that nembutsu is recitation and it does not require and understanding the profound meaning, such as "the mind is the Buddha" as found in the Pratyutpanna, "A" being the first letter of "Amida" as well as the seed syllable for the Dharmakaya, etc. Honen knew very well the depth of the Nembutsu:
JSRI wrote:According the Kanjinryakuyoshu attributed to Genshin, the three Chinese characters of Amida's name correspond to three fundamental truths of Buddhism: voidness, the impermanence of form, and the middle way between the two (Eshin sozu zenshu, 1:329). From this, it was seen that all Buddhist teachings are contained in Amida's name. The Shojukanki, also attributed to Genshin, makes this same point (Eshin sozu zenshu, 1:517). From these examples, we can see how Honen claimed that the six characters of the nembutsu ("Namu Amida Butsu") perfectly contain all the virtue of Amida's inner enlightenment as well as the merit of his outward actions.
"There is no other reason or cause by which we can utterly believe in attaining birth in the Pure Land than the nembutsu itself." This very clearly states that the nembutsu is related to the belief in attaining birth in the Pure Land. This opens up a huge narrative of "who, what, when, where, why" that is required to unpack that statement. All of these associations are brought to mind as one recites, not as random thoughts, but as part and parcel of the Amida narrative.
"...deeper knowledge" he rejects, but still mentions Amida, Shakyamuni, the original Vow, attaining birth in the Pure Land, compassion, 3 minds, 4 modes of practice, etc. He's not talking about having no understanding. We can see very clearly that he's referring to the advanced topics, such as emptiness (for which a conceptual understanding is barely a fraction of the picture), "the mind is Tathagata", "Pure Land is a Pure Mind", etc.
"...they should not put on any airs and should sincerely practice the nembutsu, just as an illiterate fool" means to openly accept the teachings as they have been presented and practice them. It refers to the understanding that more book knowledge outside of the basic narrative is not a replacement for practice.
"The Jodo Shu way of the established mind (anjin) is completely imparted here." - this is the culmination of the 3 minds and 4 modes of practice, which he spent a lot of time teaching about. He said other practices weren't necessary for these things to arise, not that people didn't have to have any idea of what they were. I already listed what these 3 minds and 4 modes of practice are before and will again below. They appear in MANY of his letters to students. In fact these 3 minds are necessary for Pure Land birth according to Shan Tao, Honen upholds this, and Shinran mentions it in the Kyogyoshinsho (it's also inherent in his statement that doubt is what prevents us from being born in the Pure Land).
Honen wrote:
But a hundred or a thousand repetitions day and night for a hundred or a thousand days can be the nembutsu of salvation by Amida's power alone (tariki), as long as one does it with an entire trust in the merits of the great Vow, looking up in confidence to Amida with every repetition. And so the nembutsu of those who possess the Three Minds (sanjin) can by no means be called the nembutsu of salvation by one's own power - no matter how many times they call upon the sacred name and as long as they are really looking up to Amida and trusting to his saving power alone.
All of these associations from the narrative become part of the recitation.
ShanTao wrote:“If there are sentient beings who desire birth in that land, they must awaken in themselves the three kinds of mind. Then they will be born. What are the three minds? The first is the sincere mind; the second is the profound mind; the third is the mind with which one dedicated all merits (toward one’s birth in the Pure Land) and resolves to be born there. If one possesses these three minds, one will assuredly be born in that land.”
Shan-tao’s commentary on the sutra states: “‘Sincere’ means ‘genuine.’ This expression is intended to make clear that the understanding and practice that all sentient beings carry out through physical, vocal, and mental activities must necessarily be accomplished with a ‘truly genuine’ mind. One should not outwardly manifest the aspects of being wise, good, and diligent while inwardly embracing vanity and falsehood.” There are two forms of genuineness:
1) Benefiting oneself
2) Benefiting others
“The second is the profound mind. The profound mind is the mind of deep faith. It also has two aspects:
1) To believe firmly and deeply that, now in this present body, one is an ordinary sinful being involved in transmigration who has for countless kalpas been always sunk tumbling in the stream of cyclic rebirth, unable to find the karmic conditions for escape.
2) To believe firmly and deeply that Amida’s forty-eight vows enfold sentient beings in their embrace and that those who without doubt or reservation entrust themselves to the power of these vows will certainly attain birth.”
“The third is known as the mind that dedicates [all merits toward one’s birth in the Pure Land] and resolves [to be born there].”
And how does ShanTao recommend awakening these 3 minds? Reciting the Buddha's name... "Our ‘nien-fo’ then becomes our vocal act; the ‘three minds’ become our mental act and our ‘benefiting others’ becomes our physical act. With this as our guide, we become ‘assured’ of our eventual birth in the Pure Land. Amito-fo."
Ven Chin Kung wrote:When reciting, one also practices the Six Principles or Paramitas (Skrt) of giving, precept observation, patience, diligence, concentration, and wisdom. When no other thought is concerned, it is "Giving." When no erroneous thought occurs, it is "Precept observation." When staying with this process without interruption, it is "Patience." When reaching one's goal in recitation, it is "Diligence." When focusing on recitation, it is "Concentration." When insight is obtained from within, it is "Wisdom"
...
I could probably quote the entire second Chapter of Ven Chin Kung's commentary from above, especially:
Ven Chin Kung wrote:One is to be mindful of the name "Amitabha," for this name enables one to reflect and intensify the same merits and virtues, thus eventually achieving a Buddha's perfection.
...
Ven Chin Kung wrote:The Ten-Recitation method is a simple, convenient effective way to practice Buddha Name Recitation. It is especially suitable for those who find little time in the day for cultivation. Practicing this method helps us to regain mindfulness of Buddha Amitabha and brings us peace and clarity in the present moment.
The OP did a bang up job quoting Hsuan Hua so I'm not going to repeat that effort.
Sheng Yen describes the various levels of recitation and how it evolves naturally through practice. Historically he's always been very Self Power-oriented (to the extent that I remember one of his students quoting him with something like "a real Chan practitioner would never rely on another Buddha") so I wouldn't expect any use of Other Power from him - but even he admits it's a progression.