I scraped all the spongy rotten wood away, doused it all in bleach to kill whatever was growing in there, and painted the entire thing with Zinsser Peel Stop primer.
Peel Stop is kind of cool stuff. It smells just like Elmer's Glue, and it soaks into peeling substrate and binds it. They do warn (duh) that this is no substitute for proper surface preparation, and I'm sure this is true, but since proper surface prep in this case would be replacement of the sill plate - a project I can't afford to repeat this fall - this approach will have to do. Ask me again in a year or two how important that surface preparation was.
Note that there are three levels of sill plate. The outer one is rotten on top, but the rot has eaten into the gap between the outer plate and the middle one that is probably the sill plate proper - by "eaten in" I mean there wasn't shelf fungus on it yet, but there was white mold with hyphae, and it had eaten a spongy cave about an inch into the wood under there. I filled it with urethane foam (yes, it is Great Stuff), cut it roughly flush, and painted over the entire thing.
The result, especially after caulking in some of the pits on the upper surface of the sill plate and painting over that, looks surprisingly functional. This is an oil-based glossy enamel; I'm using it on all the external trim. I want something that will shed water and last years. We'll see how well this lasts.
The window itself is a charming one; note that it has the same arch over it that the doors do. I assume that when the carriage house was originally built, this may have been the only actual window; the others were haymow doors, or cut later (that's my theory).
This picture also shows the roof of the outhouse. I might reshingle it, just to match, but since this is the only roof on the property I don't really care about, its priority is rather low. A bit of paint on the trim wouldn't hurt, though. Perhaps this will be an October project, weather permitting.
Anyway, I'll post a finished picture of the bathroom window after installation; right now, the final coat of paint is drying.