I have no idea what transient underdeterminism is, but I know a little bit about late medieval/early modern academic culture in Europe. What I would suggest is: abandon a quest to catalogue how many different people had theories. As you've already figured out in tracking down unpublished manuscripts, there's a lot that you won't have access to--a LOT of late medieval scholastic writing that has never been read since it was catalog-entried, or maybe doesn't even have a solid catalogue entry at all. There are just so, so many obscure scholars who have never been studied, whose texts have never been read.

You'll also want to account for how theories or models might evolve over the course of an individual's career. One of the difficulties of moving from medieval philosophy and theology to doing medieval history is that scholars of philo/theo tend to take all of an individual's work, over the course of their lifetime, and try to wrangle it into one coherent system. Martin Luther and Bonaventure are two famous examples of this. But this doesn't reflect the actual history of someone positing different ideas over time.

So rather than assert a static number--which will almost certainly be discovered faulty in the future--pick a sample group. Perhaps, pick ones whose influence on later scholars can be identified, or something.

Okay, I also found an unpublished manuscript by François Viète that advocates a modified Ptolemaic model that included elliptical deferents and epi-ellipses. So that's another one.

P.S.

After reading through back issues of journals, I found two mentions of a geoheliocentrist model developed by a Japanese astronomer. Any idea who that could be?