So the water heater is shot in the carriage house, and wonder of wonders, I found an instance of this model of water heater on Craigslist, five blocks away, new in the box, for $250. Of course, I bought it immediately. I'll install it this week. I can do the water part, but my dad will help with the gas pipe. That's something I've never done -- metal pipes. Or I might (gasp) call a plumber for the gas pipe. I'll bet the gas company would be happier if I did that.
The only problem with putting this in the carriage house is that I want another one for the upstairs in the big house. And that one will cost me regular price, and it will hurt to pay that much more. (I had been resigned to it until now, you see.)