Nosta, in Jodo Shinshu, there is no concern with reciting at the time of death.
With Shinjin, our attaining birth is assured regardless of deathbed recitations, or even any specific number of recitations. This is I suspect different than other schools of Pure Land Buddhism.
My understanding about Shinjin and Gratitude is this, and it relates very much to the passage from the Tannisho which Astus posted.
When I carefully consider the matter, my birth in the Pure land is settled without doubt for the very reason that I do not rejoice about that which I should be bursting with joy. ... If our hearts were filled with joyful happiness and we desired to go swiftly to the Pure Land, we might be misled to think that perhaps we are free of blind passion." (Tannisho, IX.)
Our gratitude is precisely because we don't have the capacity on our own to attain enlightenment, due to our blind passions and attachments, which are so deep we aren't even capable of recognizing how wonderful Amida's vows for us are.
Jodo Shinshu is all about other power, and Shinjin also comes through other power. We cannot contrive with our egos, ways of getting it. Just as we cannot contrive that we will fall in love with such and such a person. We fall in love or we don't, but we cannot contrive to make it so.
I know it is ironic to post this on a message board, but often I think we worry and talk too much about these things.
Two quotes of Shinran come to mind on this for me:
As for me, I simply accept and entrust myself to what my revered teacher told me, "Just say the nembutsu and be saved by Amida"; nothing else is involved. (Tannisho, II.)
and perhaps more to the point:
I, for my own part, attach no significance to the condition, good or bad, of persons in their final moments. People in whom shinjin is determined do not doubt, and so abide among the truly settled. For this reason their end also - even for those ignorant and foolish and lacking in wisdom - is a happy one.
You have been explaining to people that one attains birth through the Tathagata's working; it is in no way otherwise. What I have been saying to all of you from many years past has not changed. Simply achieve your birth, firmly avoiding all scholarly debate. I recall hearing the late Master Honen say, "Persons of the Pure Land tradition attain birth in the Pure Land by becoming their foolish selves." Moreover, I remember him smile and say, as he watched humble people of no intellectual pretensions coming to visit him, "Without doubt their birth is settled." And I heard him say after a visit by a man brilliant in letters and debating, "I really wonder about his birth." To this day these things come to mind.
Each of you should attain your birth without being misled by people and without faltering in shinjin. However, the practicer in whom shinjin has not become settled will continue to drift, even without being misled by anyone, for he does not abide among the truly settled.
Lamp for the Latter Ages, VI.