Jon Favreau did pop into my head as a potential, but it doesn't seem like directors really like to tackle more than one comic franchise. Bryan Singer is the only one to have done so, I think. I guess Zack Snyder too.
Singer coming back to the X-Men after almost 10 years is a promising precedent for Raimi to return, if he's up for it. I know it sounds odd, but consider:
Webb said he would like to stay on board as a consultant. Raimi had ideas for, and the desire to make a Spider-Man 4. So we could have a Dynamic Duo on our hands.
Though that depends on if Amazing 1-3 will be it's own story, with 4 starting a new plot/direction; or if 4 is the grand resolution to the first 3 films. If it's the latter, then Webb should definitely stay on board. If Amazing Spider-Man 4 is the kick off for a new story in 5 and 6, then someone new at the helm wont be as hard a sell. More than a Raimi/Webb team-up I would like to see a CBM team continue past the usual trilogy.
These films continuing in a James Bond style was always going to be the inevitable outcome of them being franchises, and a new cast and creative crew is not necessarily a bad thing in my book.
But its a bit of a catch-22.
They are planting the seeds for a bigger Spider-Man world in film, adding more villains, movies, etc. The pay off will be diminished if when those villains finally face Spider-Man, he's a different actor than who we started the journey with. It'd be best in my opinion to wrap up every dangling thread, before recasting, hiring a new director, and continuing the series; this time without rebooting.