Mine had a little problem with that until I took some extremely ultra fine sanding film to the nut on the slots and very carefully polished those slots. Tested by pulling the strings out of the slots until they came out without dragging. I would loosen to do the sanding/polishing, tighten the string back into each slot up to tune and then loosen just enough to pull it back out, checking for that least little bit of drag. But, I ordered mine from Sweetwater and specified 10-46 gauge. I also told them to make sure it intonated properly, but for whatever reason, it wasn't quite close enough. After that, no more tuning issues with whammy bar use.
You said the whammy is painful? I assume you don't mean it physically hurts your hand, right? Didn't think so, but I ordered whammy bar tips from PRS mostly for the looks to match the black pups and rings. It was too loose and I had to sleeve it with shrink tubing for a very snug fit, but it is very comfortable on my hand.
Bottom line, would you be changing the nut out yourself? Or take it to a luthier, who would do essentially what I did, but with special nut files.