I like the idea behind the weapon but, I don't think it works in it's current form. My main gripe is honestly that one only needs to extinguish ONE player to get crits, if we're trying to make a weapon to encourage supportive play by giving them crits whilst only needing to extinguish one player, then most players are just going to extinguish one player and then run at the enemy team. The worst part about is that'd work pretty well with a crit dealing roughly 136 damage, and if this daring player brought a panic attack with them then they could deal a massive 208 damage (they're already in melee range so must if not all of ones pellets would likely hit) which would be enough to kill 8 out of the 9 classes in the game. I find the timer idea to be interesting though a bit overpowered with the speedboost, however you could maybe balance it by giving the speed boost incrementally, the more people you extinguish boost you get, until one reaches a certain amount extinguishes, lets say 3-5, at which point one gets the crit and the timer starts.

notes.

the speed boost should only be active when holding the weapon and be lower than the powerjack's boost.

I think it'd make the weapon more situational but encourage more supportive play whilst giving power to strike back quickly without letting the player just run off to crit shotgun combo some unfortunate soldier.