I think you're being a bit presumptuous. You're assuming that there is going to be a reboot no matter what. I don't see it that way.
The truth is that most origin stories suffer in that they need to focus so much on the origin, other things, like the villain, don't get to shine. The Lizard is a great example. But I, and many, often give these origin movies a little bit of a pass since we understand it's an origin story, and we look forward to the second movie.
So really, the best way to make the origin story more exciting is to not do another one! Either just incorporate Spidey into the Marvel universe as is (though we know they would change the actor) and give him his own movie against a main villain and introduce MJ, possibly Black Cat, the Bugle, Empire State University, etc; or he stays with Sony (which is most likely as any deal that Sony would accept is one that Marvel likely wouldn't) and they too should get back to basics and go forward with a movie where he is against one main villain and MJ is introduced, possibly Black Cat, the Bugle, Empire State Universoty, etc.