I just had a thought (kinda based on the new leak) -- maybe the villains (Raimi and Webb) are pulled into Tom's Universe right before death, and since they "still want to kill Spider-man" like the leak said, they obviously come across Tom's Spidey and just instantly hate / try to kill him. So all of a sudden, he's facing alll these villains at once throughout the movie, and obviously will get overwhelmed, and then (maybe Dr. Strange, with/without Peter, and/or other MCU characters) go to the other Spidey Universes to "recruit" those Spiders -- Tobey and Andrew -- because Tom obviously needs some help, or maybe they think those guys will be better able to confront/fight/talk them down more effectively.
Obviously it wouldn't be as simple as all that, but just the overall all : Tom suddenly finds himself facing/fighting loads of new and other universe villains, and the good guys (Dr. Strange, Tom) realize they need to find or recruit the other Spideys to help, and go looking for them in their Universes.
Idk, pulling this outa my ***, but think it could be cool and could definitely work doing it in this way