[@Gisk] Sorry for going a bit overboard with the character stuff. I'm really not sure what kind of character I want to do, but I may make a new idea, in favor of keeping the other character isolated for better labbing. Spider Sense Lore is weird, but in Spider Verse (which includes things that not every Spider Man author deals in and that have been effectively resolved in Spider Verse,) the Spider Sense is basically seeing along this, like, loom of time thing. If you're aware of the character Silk, she has a stronger Spider Sense compared to Spider Man, and sometimes gets visions of events rather than just the typical Spider Sense thing- if I'm remembering right at least.
But, we don't have to deal in that. And, honestly, what do you think the team needs more? Because, well, since we're directly linking the powers to Spider Man, I don't have to pointedly differentiate from Spider Man, which is what the no wall crawl was about. My most fleshed out idea is of sort of a team-relay guy. He'd be a varsity athlete at Garfield (maybe a wrestler or something,) who would contract the spiderflu, and only get Spider Sense. So he has to deal with the adjustment from being very active and forward at school, to doing a support role in hero stuff when that comes around. I think it'd be an interesting personal dynamic, and having a "command center" guy/communication relay would be interesting, complete with walkie-talkies.
The other idea is basically pure spider-based offense, claws/talons akin to Spiderman 2099, tarantula bristles, and maybe fangs.