So it is the headset bearing. Sounds like the lock nut on top is/was not locked and the adjustment tightens up when turning to the right. That should not happen... something may be adrift.
Was thinking along the same lines. My guess was that the lock washer was missing between the lock nut and bearing cap(or whatever the technical term is). Turn it one way, tightens bearing. Turn it the other, loosens bearing. The lock washer is usually keyed to keep it from turning. If this is the case, I'd go over the entire bike with a fine tooth comb.