Curious, if you tune up, use the bar and then check the tuning, are you sharp or flat? And which strings? You have to keep in mind that locking tuners and a locking bridge are not equivalent. With the locking tuners the strings still move across the nut, and thus can get hung up there and end up sharp.. What provided trem tuning stability for me was working on that. If the strings aren't moving at the tuner, then they're probably sticking at either the bridge or the nut, and the nut is usually more likely in my experience. And a lot of really expensive guitars I try out still have really suspect nut installs.
First I'd see which strings are out. I've worked on a few and a lot of the time it's the 2nd, 3rd and 4th, in that order, that hang up. Not sure if you're decked or the bridge is floating, but if you pull up a touch on the bar and release, do they come back into tune? If so, it's probably the nut, and when you pull up you're moving it back from the spot the string got hung on.
From there you've go some things to look at and decisions to make. If you want the easiest DIY remedy and lowest hanging fruit, get some ground up pencil lead and Chapstick and mix it into a paste. Dab a little into the nut slots of the problem strings and work it in. If it's better after that, even if it's not perfect you're on the right track. Unless you've got a Graph Tech nut, in which case lubrication isn't the issue.
From there you either need to check the nut or get somebody do it for you. The things to look for are whether the slots are too tight or seems to be sitting up on the rear of the nut. And at worse case is making contact at the back and barely or not touching the front. This happens more than you'd think. Mine are adjusted so that the main contact is at the front, the back of the slot drops away at about halfway back into the slot, and there's a slight fan out at the rear sides, so if you look down at it it's kind of in this shape \/. This is so the string doesn't catch on the sides if it's not in a perfect straight line to the tuner. If the nut's really high that can also cause issues. And I didn't recall seeing whether there were string trees or staggered tuners involved so that can impact what you look at.
Stewart MacDonald used to have a series on small jobs like this so you can check their site archives. That'll have pictures that illustrate the above. But it help if you have feeler gauges and files on hand before you go f**king with the stuff.
Other thing to consider is one of the Zero Glide nuts. They've got a combo of a nut to keep the side to side stability and a zero fret. I just ordered one to try out but haven't got it installed yet.
And some of this depends on your bar use. I don't go real crazy with the it. Mainly minor flutters and dips, with an occasional upward. And I use one of the Super Vee Mag Loks as well. It takes a while to get to the point where I have to retune. If you're really overboard with the bar and wind up with the stings flat on the fret board, just my .02 but you're probably going to need to go to a locking nut unless you want to have to make adjustments. Although as I mentioned, if you can incorporate just pulling back a little bit after you're done spazzing out, it usually puts things back into tune. I did that for years until I started messing with the nut.
