“More specific” prompts are given in both of the first two rounds, as the host sees fit.
Final Jeopardy responses are written down, and if you’re not specific enough the first time, there’s no second chance. In the past, when the final category was about US PRESIDENTS, they’d sometimes tell contestants “be very specific”, which was as much as to announce that Adams, Harrison, Johnson, Roosevelt or Bush would be at least part of a correct response. I understand they’ve revised their practice to say “be as specific as you think you need to be” whenever it’s about presidents (and maybe when it isn’t?) , but others here may know better, so please feel free to correct.
In this case, I’m confident C of E or Anglican would have been accepted. I wouldn’t expect them to announce what other phrasings would have flown, because what for? while it would have the potential to set an awkward precedent.
Finally, since we’re here and not somewhere else, “had got”; not “would have got”.