Sterling Majesty: Trem Arm Knocks Inside Hole

Question for anyone familiar with the trem arms on the Sterling by Musicman Petrucci guitars: Is there any method to have the trem arm fit tighter inside the hole other than by tightening the adjustment allen screw?

My issue is that I’ve tightened the adjustment screw, but the trem arm still knocks back and forth at the bottom of the hole. I think the only feasible way to stop that is to thicken the bar at the bottom, by putting some type of teflon tape or similar material on it. Curious if…

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