Just lock it all down. You enter the adventure with 3000HP, no matter what you are wearing, every gun does 250 damage, no matter what you actually equip, your dodge/aim chances are exactly x, modified by distance or whatever, then you let it all be about the play and teamwork...
I keep thinking about chess. Everyone starts off with the exact same pieces, it's their skill that dictates who wins, nothing else.
Only problem is the luck factor, if one player in your team is 1 round too late or goes afk that's enough to lose the entire game.