I believe I have found the issue. It appears that there is a defect in the Hall sensor that is causing a double-spark: one at TDC and the other about a third of the way to bottom. I removed the Hall sensor and positioned it higher (so only the bottom would be near the magnet on the rotor), adjusted the timing so the now-single spark would fire at TDC, and it seems to be running like a champ.
On a side note, the folks at stirlingkit had no interest in helping with this, or with providing a replacement ignition system. They only offered me a 15% discount on a future purchase. There are other companies that sell these little engines, so I'd encourage you to patronize them rather than stirlingkit.
I appreciate all of the suggestions and feedback that you folks provided.
Dave