JustinInMN
4 of a Kind
With that in mind, I'm gonna go nuts and go for an overbet shove. You bust either way if you're behind, but an overbet shove may look like enough of a bluff that Villain may just snap it off with a bluff-catcher.
My concern here is you let the Ax or random -x hands get away that may call a small sizing. If we overbet we are really hoping to be against exactly AJ or hoping the villian isn't terribly price sensitive.