The remaining OAM priority issues can be fixed by only checking the priority of the topmost sprite against the backgrounds.

Passage in Anomie's Register Doc:
Code
Note that only the priority of the topmost sprite is
considered relative to the backgrounds. Thus, if FirstSprite+3 and
FirstSprite+4 are identical except FirstSprite+3 has priority 0 and
FirstSprite+4 has priority 3, they will both be hidden by any backgrounds that
hide priority 0 sprites. This may seem counterintuitive, since FirstSprite+4
would normally go in front of these BGs, but many games depend on this
behavior.