Update on Tom's batch:
The beer was in secondary, "bulk aging," in a carboy. But the SG wasn't dropping. I finally went and bought a belt heater and carefully draped it around the carboy, and used a sanitized turkey baster to stir up the bottom every few days. It raised the temp alright, but having racked to secondary before fermentation had advanced nearly far enough, I was fighting an uphill battle to get the SG to go down.
But eventually, in about 4 weeks, I finally got the SG to reach just a point or two over target. So then I bottled it, a few days after Christmas, which means the beer was about 3 months fermenting, total, or about 2x the hoped-for schedule. Lesson learned: Next time I do this I will definitely do a gravity reading while still in primary and not rack unless it's nearly fully fermented.
I built a platform with a hollow space under it, and put the bottles in boxes over that in my closet, and put the belt heater on the floor underneath (in the hollow space) hoping the additional warmth would help the bottle carbonation occur, as it is otherwise too chilly in the house in winter. Three weeks into this process, I took one test bottle, chilled it in the fridge for 3 days, and tried it.
Pretty tasty, but practically no carbonation or head to speak of. I'm guessing that once again, my temperature is too low, which I believe was an issue during secondary "bulk aging" as the SG was way too high for much of this period, and now the bottle carbonation isn't happening very fast. So I'll keep the bottles in this "warm" chamber a few more weeks and try again.
Probably there's a lot about high SG beers I need to learn first.