If the strings are moving sharp, then the spring tension is superior. If the bridge continually lifts, the strings would be moving flat.



The bridge can still continue to do what it has a predisposition to do, independent of the neck and vice versa. The final stages of a setup is what should be keeping all of this in check.



No nut grab is equal to tremolo spring pull. Consequently, tightening the claw can indeed oftentimes obliterate certain nut grabs. It is a case of superior PSI vs. inferior PSI.

Granted, and I surely do see your point, it can be just the nut and oftentimes, such circumstances do indeed dictate this as the stand alone malady with your's being the stand alone remedy. Yet, based on my interpretation of the OP's complaint, it appears in his case to be a combination of a few things. Sight unseen, all we can do at this point is surmise, based on our own experiences.

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You dig?

I think lubrication may be the issue. During a string change, I lube the nut, saddles, the two points where the trem springs connect with 3in1 oil. I grease the underside of the string tree(s) with lip balm.

Perhaps the strings are hanging up on the internal components of the bridge assy. I've heard of techs using those small red plastic stir straws that come with a cocktail and run the strings through small sections of the straws during installation to prevent this.

I use a silicon based lubricant on everything. Just my $0.02.