I doubt you have the orientation of the bearing cages wrong. If they were, you wouldn't be able to get the fork both tight and turning smoothly from side to side.

You mentioned the sequence of tightening your headset, but not the tightness. The locknut has to be TIGHT against the upper bearing cone. You need to hold the bearing cone with a thin headset wrench as you tighten the locknut against it. It usually takes a couple of tries to get both the cone and locknut tightness right.