OP stated he rebuilt the carb "a few years ago, and it has very little cumulative run time". I was in the same situation and rebuilt it again. The power piston was OK - I just needed to clean off the white powdery residue on it.
I think that these things need to be run regularly to keep them from getting stuck. Maybe something like Sta-bil 360 would help.
I pulled it apart and degunked it before my recent round of work. The piston is not seized or stuck. It moves, just wondering if it moves freely enough.
