This thread was very useful in helping me deal with two pipes that had broken off tenons stuck in the mortises. The screw method worked for one tenon, though I used a deck screw like the one shown in this Rebornbriars article
. Also, I used a slightly different technique. I turned in the screw until it had good grip but was not very far into the tenon. I then placed the stummel into my freezer for a few minutes. After retrieving the stummel I gripped the screw head with pliers and twisted clockwise while steadily (and gently) pulling the tenon out. This worked like a charm.
The second tenon was a different matter. The technique that worked so well on the first tenon got me nowhere with the second. The suggestion by ejames to use a coping saw to cut through the tenon gave me an idea and kept me from despair. I used a coping saw blade to cut a slot into the tenon, periodically applying Everclear around the tenon. When I had a well-defined slot I inserted a small slot screwdriver and turned clockwise while subtly working the tenon out of the mortise. I do not know if the Everclear loosened the gunk seizing the tenon, but the tenon came out easily with the turning of the screwdriver.
My thanks to ejames and the other contributors to this thread - may it be useful for another two years!