[QUESTION] Music man tuning stability

So I have a JP13 that I really like. But I've noticed a problem with the tuning stability.

When using the tremolo arm to dive bomb, when I come back up to pitch the low E string (heavy E string) will be sharp. All the other strings will be 99 or 100 percent in tune. It's just the biggest string that's the problem. And when I pull back up on the tremolo or do some shaky bends on the low E it will mostly return to tune.

I've tried heavily lubricating the nut, saddles, bridge posts and knife edges, and changing strings. I use 10-46 in standard tuning and the guitar is set up perfectly. I've set up many floating tremolos and like to consider myself knowledgeable on them. But I cannot for the life of me figure out what the problem is. It seems like the only explanation is its binding on the nut but I don't see how or why?

Any ideas would be greatly appreciated.

submitted by /u/CakeJollamer
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Source: Guitar