One caveat:

When I said that there was no problem with the linear voltage regulator at "U4" on the Betz board, with 5v left floating and 3.3v on the BATT line...

I'd already tried replacing that linear voltage regulator with another 2.5v one from Digikey since I a had a package of them from trying to fix the last Betz board. It happened to run at 2.6v instead of 2.5v and that actually solved some of my problems but not all of them. Then I said screw it and decided to go all the way to 3.3v.

In other words, my successful results are based on that U4 having been replaced with another model of theoretically the same specs.

So what I'm saying is, take my results with a slight grain of salt and check your own chips for heat before committing.