Recently acquired Majesty and JP tuning issue

Both of these recently acquisitions show the same behavior. I can tune them up to be pretty stable with the bar, but if I do some big bends (step or step and a half), the string goes flat. After it goes flat, if I dive the bar and release, it comes back pretty much in tune. Anyone else seen this behavior with EBMM trems. A Google search turned up a few forum post that claim this is caused by binding at the saddles vs the nut. I’m wary of lubing the saddles because of the piezo. Anyone have any thoughts on this?

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