For a universe-hopping Sinister Six, you could have Otto Octavius aiming to find a world where his wife is still alive. But you'd have to reverse the end of Spider-Man 2, or just say that he survived and escaped off-screen. It's been 16 years, you could swing that. Yes, you're taking Kingpin's storyline from the animated film, but they're fine with going straight into the spider-verse anyway.
Doctor Octopus (Maguire)
Mysterio (Holland)
Scorpion (Holland)
Vulture (Holland)
Electro (Garfield)
Rhino (Garfield)
Foxx and Giamatti weren't great versions in ASM2, but they're good actors and had such limited roles/development you could practically reboot them.
Maybe at the end of it all, there's a Master Planner who first gave Doc Ock the impetus to travel the spider-verse, etc. Norman Osborn? I know MP is traditionally Octavius, but maybe it could be a bait-and-switch thing.