I wouldn't go as far as saying Incredible Hulk has any connectivity to Ang Lee's movie. Ultimately, Marvel appeased everyone by saying the movies could be connected, but never that they were. They just knew they couldn't tell another origin story. These days, I doubt they'd play it as coy.
The Amazing Spider-Man movies would never get the same treatment, regardless, because Marvel would be locking themselves into the Osborn and Electro origins, as they appeared in those films.
I'm sad for Garfield. He deserved a better legacy. I still think, baggage and complications be damned, that Marvel should give him a shot. As bad as those two Amazing films may have been, Garfield and Emma did well enough to distract you from the nonsense. They truly were some amazing finds. I hope they can find someone half as charismatic for a Spidey replacement.