OK, I have some new information about this - it’s not related to the Google Play Services sign in at ALL.
Doing some testing on a bunch of different things last night / this morning, trying to get a build that worked (nothing did - I tried every combination of Android settings I can think of), I occasionally did manage to sign in (it has always been possible ~1/5 times) and get into the game proper (at which point, everything’s fine and you can play the game for as long as you want).
UNTIL you try access the achievements. Or you lock the phone and then unlock it again. Or anything else that takes rendering away from the game. You can browse the achievements list for 3-4 minutes, going in and out of sub panels, but the second you close the panel: Crash.
I went back to an older build of the other project and confirmed that, yes, you can lock the phone as many times as you like and it won’t crash. So something changed in 4.10 that causes this problem.