As for Apple-II specific details (graphics chipset etc.) someone else will need to chip in - never even saw an Apple-II during my childhood, Norway like much of Europe was Commodore dominated.
This made me laugh. The words "Apple II" and "graphics chipset" don't belong in the same sentence! The Apple II graphics were a fantastic, and fantastically weird, low-hardware hack.
That does sound rather strange. But fascinating...
Stuff like that seems like it might explain some of the mutual disdain that Chuck Peddle and Woz seems to have ended up with after their early encounters (when Peddle was on his 6502 "sales tours"; though maybe interviews and books have exaggerated it).
I can totally see this being the type of hack that would excite someone like Woz to pull off but that would make Peddle's straight laced inner formal engineer rage... Combine Commodore / MOS engineerings early problems getting a decent color graphics chip together but cultural refusal to go for something more hacky (the did plenty hacky stuff but only when Tramiel put jobs on the line) to get out the door quicker, with plenty of blame being put allocated to Peddle on a regular basis, and I can see lots of ego getting caught up in it..
IIRC, things were even better. There were two (740 byte, IIRC) buffers from which samples were taken at every horizontal refresh.
The sound driver used one to get samples to send to the speaker; the disk driver used the other to control the rotation speed of the disk drive (using pulse-width modulation).
Apple II assembly coder here, and the book I used is in your second link, "Using 6502 Assembly Language" by Randy Hyde. Mine had your link's cover, not the cover shown on Amazon:
