Ah! The woes and traumas of double-locking jobbys. I suggest checking Rich's tech page at Ibanez Rules.
Could be a wide variety of things... check Knife-edges, post valleys, check the locking nut is secured/holding the strings in place (but don't overtighten!), could even be something as simple as your new strings needing stretched in.
One interesting note is the trem was blocked. It's likely your springs have developed a "memory" with being static for a long time and now that you are using the trem the springs need to be broken in again. If the trem isn't used, the springs are static and can form a "memory"... I had this when my Ibanez was newish. I didn't use the trem for weeks and then when I started using it again I had some bizarre tuning problems... then as the springs got broken in again the problem disappeared. The solution is to use plenty whammy, all of the time
That could be your problem.
Let us know how you get on.
'87