Try this, i never use the trem on my guitars. So i lower the tailpiece closer to the bridge plate, and wrap electrical tape around the bridge post, just enough that the bridge slides back into the post with no effort, but doesnt wiggle once its seated.
I have always done this easy procedure, and the guitars stay in tune very well.
Never hurts to try it.
that way you wont have to redrill for tuners and all.
