Floyd Rose? There's your problem right there. :p
I don't understand how what you describe is possible with a recessed bridge. When you say the front is hitting the paint, you mean the side of the trem nearest the pickups, correct? The only way this occurs is if your trem is so low that when you drop the bar the bridge rotates into the paint. I've seen this on non-recessed bridges set too low to the body, but never on a recessed bridge.