This is something I've been trying to figure out for a little while now, and I think I've *finally* traced the problem to the string retainer bar.
Basically, my high B and High E on my Suhr 7 tend to "stick" while I'm tuning - I'll twist the tuning peg and the pitch will remain stable, remain stable, remain stable... and then suddenly jump or fall sharply, way overshooting my target pitch. In some instances, while tuning up, this results in snapped strings, which if you're using Elixirs is a pain in the dick. The G through low B strings are fine.
I thought it was the tuning pegs at first, but last night while restringing actually bothered to closely watch the pegs while tuning, and sure enough they're rotating as they should be; the issue is that the string is "sticking" at either the bar (or, possibly, the nut - which, it should go without saying, is unlocked).
So far, I've tried swabbing the underside of the bar with a dry-formula PTFE-based lubricant (I have a good dry formula penetrating chain lube that I figured would be perfect for this) which didn't seem to make a huge difference. Last night I tried backing out the retainer bar about as far as I could to lessen the angle/pressure on the bar, which helped somewhat, though given the headstock offset it's still a fairly steep angle. I'm thinking longer screws might help, if I can find a direct replacement.
Has anyone else had this problem? Any other suggestions I should try? It's not the end of the world, exactly, but it makes the already-fun process of tuning a Floyd a little more laborious.
You could run some slim plastic tubing over the string where it goes under the retainer bar, similar to what some people do for the break point on strat bridges. Big Bends String Sleeves | Musician's Friend