This is a follow-up, in case anybody has similar problems. In brief:
- I've ended up getting the best results with the Thro42 variant of the TFT35-E3 firmware; however....
- Contrary to the documentation, I need to use "M575 P1 S1", not "M575 P1 S3" (plus "B{baudrate}") in config.g to enable support. Using "S3" results in flaky behavior.
- The Thro42 variant (as well as its immediate predecessors, the bcmob and JimmymadDness variants) disable the ability to print from the TFT's own SD card and USB slots. They also lack some of the more recent feature additions of the main BTT branch. OTOH....
- The point of these forks is to enable RepRapFirmware-specific functionality, including the ability to start prints from files stored on the mainboard's micro-SD card, a print status screen when a print is underway, and (for the Thro42 variant) the ability to run RRF macros. These features more than make up for the ones lost.
It took me many hours of experimentation to get to this point, so I hope these tips will smooth the way for somebody else.
Note also that the BTT github page for their TFT-series displays is quite active. Somebody recently submitted a merge request for some changes to improve RRF compatibility, but those changes don't come close to doing what the Thro42 fork does. It's possible that a future merge will do so, though.