did you measure the shims that are in there now to ensure they are both the same size? the kit comes with 2 different sets of shims for the head (the shims between the damper and the radial bearing...
no, this is not normal to have to shim one side and not the other, in fact, that would cause you issues.
if a bearing was sticking and not seating all the way down, it would actually get the heat too tight, not leave play, so something is amiss here. we just need to figure out exactly what it is.
what dampers are you using? synergy, or trueblood?