Hi Matt,
I wonder if you are looking too deeply at the problem. I wonder if the issue confronting the Parish Priest is simply one of finding the time to undertake that research on your behalf. I wonder if you have gone to your local Priest and offered to volunteer some of your time to transcribe any or at least one of the local registers.
Once you have shown your local Priest that you not only know how to read those older styles of handwriting, but also that you know how to conserve the registers, then your local Priest may well be prepared to support your request of that distant Parish Priest, and ask for him to provide you with access to those registers that include your ancestors records. Of course, in either instance, there may well be expenses that those Parishes may need covering, so it is always sensible to couch your requests with an enquiry as to any fees or charges that may apply, or the details of their current program for donations.
When I have needed access to Church Registers, I have found that if I offer to transcribe part of a register that has not yet been transcribed, that there is a great deal of co-operative efforts among everyone at that particular church. I am in NSW Australia, and once I have gently provided evidence that I can read the 19th Century long hand, AND assist with conserving the register, I have not ever been denied assess to a register. I have transcribed various registers for denominations including Roman Catholic, Anglican, Baptist, Methodist, Presbyterian and Salvation Army. Some registers have been found (by me) as door stops, foot rests, stools to stand on. Once the locals understand that I am not interested in complaining about past treatments of these registers, but more about saving the records, and that I am willing to give my own time, then I have not met any difficulties at all.
I usually approach via the denomination's local church (local to me), where it is likely there will be members of the congregation who know of my volunteer work in several different organisations in our local community. They in turn are in a better position to introduce me to the person holding the actual register I seek. In NSW Australia, many registers have been transcribed by various Genie societies, and also by the LDS. But not ALL .....
Cheers, JM