As the world turns, my saga is not yet over. I ended up talking to a very competent nurse on the Living Donor Team, as I wanted to know the reasons for my rejection. They are, first, I periodically take ibuprofen, and second, at long intervals I have used meglimine flunixin to treat joint pain. (This is -ahem- a livestock drug. The nurse did not seem to share my belief that "cows are mammals, I'm a mammal, so no problem"). At any rate, if I stay off those two for a month, my potential donation status could be reconsidered.
A logistical problem I would need to address is that I live by myself, and my cat doesn't drive, so post-donation care is something I would have to think through carefully.
Just an update, as there are members here who have been helpful to me as things have gone along.