I had a similar problem with my 03' Jem 555.
I didn't notice how extreme the problem was until I took it with me to a gig & checked it with my tuner after every song.
Everytime I used the damn bar, or even looked at it funny, I would be out about a 1/2 step. Not just a few strings...the entire guitar!!!
Needless to say it didn't finish out an entire set & has been retired from live situations.
Maybe it's all in my head, but when I started cutting the ball ends off again it seemed to stay in tune better.
Plus I took it out of E flat & left in in E. That seemed to help too.
For some reason that guitar HATED E flat.
My RG 550's that I gig with constantly never have that problem....
However, they also have the locking stud design that the new trem lack.
I'd say try NOT leaving the ball ends on....
Also swearing profusely at your guitar might help slightly
Works for me