I have some #2 victor coils that are getting a little weak for NY winter trapping. I was planning on putting four coil kits on them, but I saw that it’d be cheaper to just replace the springs. I’m thinking with music wire ones. Any reason I should four coil instead? The traps are pretty much stock, no base plates or anything.

New springs should be plenty IMO, no need to 4 coil such small traps. 4-coiling is really just for helping bust up through a thick crust of dirt and you can't cover a #2 trap with that much dirt or you'll not have enough jaw above ground when sprung to get much of a hold on the critters. Once a trap is closed the levers locking up keep the jaws from opening, super strong spring strength isn't needed.

This! No real need for oversized springs either. Stock springs are usually cheaper and are plenty strong.