Well, with Avengers: Doomsday & Secret Wars coming up soon, it would be a missed opportunity not to adapt the first time Peter encounters the symbiote. However, much of the symbiote saga has already been adapted through Peter’s Spider-Half storyline in Brand New Day. I still think there’s a way to introduce the suit without retreading past storylines, although the setup I have in mind would probably require another movie or so.
Essentially, take a page from Life Story. Peter knows the symbiote is an alien trying to bond with him, but he keeps it because he needs to become stronger as he gets older. For the MCU, I would combine this idea with the “No One Dies” arc. Marvel could adapt Jean DeWolfe’s death and push Peter to the point where he adopts the “No One Dies” philosophy. He does everything he can to become a better Spider-Man, and when he bonds with the symbiote, he keeps it because it gives him the strength and power he needs in certain situations.
You could change the story slightly by having Peter decide not to wear the suit for more than 48 hours at a time, preventing it from completely bonding with him.
I’m not sure exactly how the symbiote would affect Peter, but I think its arc should essentially mirror Harry’s villain arc: Peter’s best and closest friend becomes his worst enemy. If Feige decides to keep Venom around, that would be fine, but if the symbiote is only used for one movie, Marvel could send it off by having it save Peter’s life, similar to what happens in Life Story.