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I recently got an offset with the locking floating trem (TVL JM)-

I had a VM Jag before that and never had to deal with setting the lock.

According to some stuff written about this trem (and youtubes), the tension screw should be loosened just to the point where the lock can move in and out on the plate with just a hair of tension clicking it in place if you want to use it. The problem I'm encountering with it set up like this is the screw/spring is unwound so much that portion of the tremolo bottoms out in the cavity with almost no dive- maybe a half step worth of movement down.
The trem arm seems to be in the correct spot but the tremolo is almost useless like this- is that normal? Do people usually forgo 'correct' setting of the trem lock on these? Or is there something that can be done like cutting the screw down a bit?

I never use the locking screw. Notice, mastery removed it entirely. Nothing should be loose, sloppy, or getting in the way. Sounds like you've over loosened everything. When I have used the lock, I just push down slightly on the trem arm, and you can slide it easy. I'd tighten the screw back up to where you had it. That being said, I like my screws and these trems stiff [twss].

I investigated wrong, the trem arm has been manufactured wrong or something with these trems and goes too far past the end of the collet and thats whats bottoming out. Seems to be an issue with AVRI trem systems.

This changed my life http://staytrem.com/Page-/-Category

The arm won't protrude through the bottom of the collet, and shouldn't bottom out.

2 birds with one stone, one bird you weren't even aiming for!