I think I figured this out. The exhaust pockets are quite shallow, about 0.1". So with 0.060" shim I'm already using the most of the pocket and the cup is starting to dance more and more the higher I'll lift it from the bottom of the pocket. Intake pockets are much deeper. So my options are:
-Shims in the cup
-Accept more assemled hight and lower spring pressure
-Get retainers that will eat up the assembled hight more