Jim,

There is a pin and "V" slot that centers the nose tire when fully extended. Put the AC on jacks and verify that when the nose gear extends it properly "cams" to the centerline.  Try turning the nose tire when fully extended.

I know of one pilot who taxied over a rough spot on the ramp while turning. The action forced the centering mechanism to be misaligned to the point that the nose gear jammed in the well and would not extend. He made the evening news but was otherwise unharmed in the "nose gear up" landing.

I am thinking you have a milder case of the same problem and that the alignment pin jammed in the slot due to the high turning moment and then released when there was sufficient braking action to cause enough down force on the nose gear.  This may have also straightened out your turning mechanism so you want to try to turn the nose gear while extended to be sure there is minimal play and no hysteresis.

Regards
Brent Regan