I have to confess to being flabbergasted by your suggestion that on the basis of SN 22.56, "kāyasamphassajā" will have to be limited to only the contact-triad of body, body-consciousness and tactility, to the exclusion of eye-contact, ear-contact, tongue-contact, nose-contact and mind-contact.
Since you applied this restrictive definition of "kāyasamphassajā" from SN 22.56 to SN 48.38, I think it would also be legitimate to apply it to the Uppapatika Sutta in SN 48.40. Going by your proposition, this would mean that -
In 1st Jhana, with the cessation of the pain faculty (which you limit to "body" pains), painful eye, ear, nose and tongue feelings will persist (since these don't arise from "kāya"samphassajā).
In 2nd Jhana, with the cessation of the displeasure faculty, painful eye, ear, nose and tongue feelings will persist.
In 3rd Jhana, with the cessation of the pleasure faculty (which you limit to "body" pleasures), pleasureable eye, ear, nose, and tongue feelings, AND painful eye, ear, nose, and tongue feelings will persist.
In 4th Jhana, with the cessation of the joy faculty, pleasureable eye, ear, nose, and tongue feelings, AND painful eye, ear, nose, and tongue feelings will persist.
At nirodha sammapati, with the cessation of the equanimity faculty, equanimous, pleasant and painful eye, ear, nose, and tongue feelings persist.
I think it should be quite obvious that your limiting kāyasamphassajā to only the contact-triad of body, body-consciousness and tactility in every context will have very non-canonical results. I'm not suggesting that SN 22.56 is wrong. On the contrary, I'm of the view that the analysis in the Khandhasamyutta cannot be applied verbatim to the Vedanasamyutta and Indriyasamyutta analysis.
SN 22.56 is a very fine analysis of all the 6 types of contacts that are possible. It distinguishes each of the 6 contacts from the other 5 contacts. On the other hand, the relationship that is explored in the Vedana- and Indriyasamyuttas deals with how feelings/vedana (the simple affective khandha) gives rise to emotions (somanassa/domanassa - the experience that is certainly broader than simple affective vedana). SN 22.56 deals with vedana inter se, which SN 36.6 and SN 48.40 deals with feelings versus emotions/moods. It would be quite inappropriate, in my view, to appropriate a technical term used in one specific class of vibhanga and applying it indiscriminately to an unrelated vibhanga.
I think it is not logical to assert that SN 36.6's analysis of kayika vedana is restricted to vedana arising from the contact-triad of body, body-consciousness and tactility. If you are correct, this must mean that the 2nd dart can never arise from eye-, ear-, nose, or tongue-contact. It should be obvious then that if your analysis is correct, this would imply that putthujanas would never generate any form of anusaya whatsoever based on feelings flowing from eye-, ear-, nose-, tongue- and mind-contact. This directly contradicts SN 36.6's description of raganusaya that flows from delight in the sensual pleasures. Just because the 2 Sick Ward suttas are appended, there's no reason to argue that their example excludes the universe of the other 5 contacts.
Coming back to MN 137 and the plausibility of a mental kayika vedana therein. Yes, certainly I would agree that the sukha which arises "when one regards as an acquisition the acquisition of forms" is vedanā born of cakkhusamphassa. But that was NOT my point. I referred you to the other contact established "when one recalls the previous acquisition of such forms after they have passed, ceased, & changed". Seeing acquisitions will certainly give rise to cakkhusamphassa; recollecting acquisitions can only arise from manosamphassa. I would like to hear your thoughts on how "recollection" (memory, a mental dhamma) can conceivably form cakkhusamphassa with eye and eye-consciousness.
You said -
"Cetasika vedanā (sukha, dukkha, or adukkhamasukha) is the vedanā simpliciter born of manosamphassa".
I think this sums up the crux of one of the elements of our disagreement. I'm of the view that cetasika vedanā is NOT the vedanā simpliciter born of manosamphassa, but the complex range of emotions that are felt on manosamphassa's 1st Dart. Based on my understanding of how SN 36.6 intersects with SN 48.36 - 40, cetasika vedanā has to be more complex than vedanā simpliciter. Cetasika vedanā is marked with qualities such as sorrow, lamentation, grieving, weeping, breast-beating. Essentially, that's domanassa, rather than the simple experience of pleasant, painful or neutral.
I'm happy to say that I fully agree with your points on MN 38 and MN 148, with a tiny reservation as to whether or not feelings bear some culpability for suffering. But just because their soteriological denouement lies in their cessation analyses does not mean that their arising analysis is not relevant to the issue of whether there can be mental kayika cetana.