After lots and lots of attempts at trying to figure out why exactly my Ibanez S570b was going out of tune whenever I used the trem, I think I found the problem. It wasn't the actual trem that was going out of tune, in fact it was probably "holding tune" just fine. It turns out that the neck seems to be shifting in the neck joint, causing the strings to go out of tune.

The problem is, I've tried tightening the neck screws as tight as I can, but not matter how tight I turned it, the neck still seems to make a creaking noise whenever I push or pull up on the trem. Anything I can do about this?
Make a small shim and put it in the outer half of the pocket to stop the guitar from shifting up and down which is what I assume the issue is considering the tremolo is changing the tension on the neck. Then adjust the truss rod and bridge to compensate for the little bit of difference in action the shim will cause. Good luck.
Something like a cut up credit card will do the job
Shecter Omen 6 with Seymour Duncan SH-6
Epiphone Les Paul Standard
Fender Frontman 25r (crappy)
Digitech HardWire TL-2 Metal Distortion (Makes the amp sound not shitty)