Normally it's hard to actually see the stab fluttering. It'll usually transfer it's oscillation to the weakest link..being the elevator.
Bracing is a good option, but I'd hate to see you drill holes and what not in your stab for anchors and discover it didn't help.
4-40's look small on a big bird aye ?
I would still seriously think about ball links instead of z-bends at the servo arm. It'd be an easy fix. They may feel snug but the extra precision in a ball link might just be enough to eliminate the flutter. What servos does the guy have you mentioned ?