The problem with your thinking is assuming some other facrep at your chosen facility is going to want some other facreps problem child, and as has been rumored, your NATCA status may or may not be taken into account already. With reps having a say in this, it's a risky move.
I say this as someone who had a contentious relationship with his facrep/management at my time of departure from my previous facility, it definitely followed me and was something I had to overcome to a small extent to restore my good name when I got here. Shit like that will be discussed and it will follow you, and now it's just one more thing to get in order on top of training, learning who is who at your facility etc....
Frankly NATCA has been dropping the ball on some big deal issues here of late and getting out of NATCA is justified in my eyes if one wanted to do so, but doing it just to game the system seems like a bad move.