Even after re-reading the horcrux stuff a couple times, I'm still confused.

There are two types of horcuxes, v1 and v2. v1 only captures your mindstate as it was at the time of creation. v2 updates all horcruxes to the current mindstate. v1s were hidden in the canonical places (diadem, slytherian's locket, etc), v2 in the hard to reach ones (mariana trench, pioneer probe).

After 10/31/1981, Tom's mindstate bounced around the v2 horcruxes. In 1992, Quirrell found a v1 horcrux ("one of my earliest"). How does that work? How can a v1, which hasn't updated, give rise to the current Voldemort?

He wouldn't have Slytherin's monster's power, or knowledge of anything after the horcrux's creation.

Also, how are those current v2 backups handling two Toms? Which mindstate is getting backed up? Probably the QQ one, but how does V know the system even works??

And isn't it suspicious that Quirrell finds this horcrux just a few months before Harry is to attend Hogwarts?

Upon rereading 108, it's ambiguous if QMort is telling the full truth about horcruxes. His Parseltongue confirmation comes later, after his horcrux explication.