Ok - so, I can't get this reliably working at all on one of my locks.
The Assure that seems to work well consistently has a "module firmware version" = 5.
The Assure that does NOT work has a "module firmware version" = 7 (newer!). On this lock, I can't get any LAST_UNLOCKED_BY programming to trigger, even though the logs indicate that it should. I guess I'm going to try resetting/renrolling/etc - which sucks because it's sort of a PITA.
All other settings are the same.
@RyanE - do you have any Assures? If so, do you have any issues on any of yours like I'm describing? Thanks for your help!