Hey Driz,
If you can recall I used to have 2 Gretsches both with Bigsbys. It was wayyyy back when you and I 1st started to play together at Southside. I used it for the same kind of stuff you want to use yours for and I remember you always digging it. I rarely had tuning issues. If anything after a long while it would go a touch sharp. that was my SilverJet that had a nice roller bridge and nice nut.
Now my Brian Setzer 6120SSU was bone stock and was less stable. I have never used a tele w/ a Bigsby, but you can have a Gretsch set up to be more stable with them. I assume the same for a Tele.
Oh BTW..... Remember these?!?!?! Boy if only I still had the SilverJet!!!