I finally got ahold of someone at Yamaha. They sounded surprised that my nut had broken ... and apologetic about not having parts available. It seems they only keep spares in stock for about ten years and don't have lists of dimensions for the parts they do stock, and this guitar is just over a quarter of a century old. But a technician cheerfully stayed on the line a while to give me advice (where I might be able to find a close enough third-party nut and enough detail to figure out which one to get, the difference in sound between carving one from scratch out of bone versus carving it out of brass, fitting the slot widths to string guages), and I found out that the cheapest current model similar to mine in their FG series only costs $300 -- a hundred dollars more than mine cost in 1980 (making me wonder what a "1980 dollar" translates to in today's money). If my guess about the model numbers is correct, a closer match would probably be the $400 model.
I'm not considering replacing my guitar (having a professional luthier make me a new nut if I give up on doing it myself would only cost $50, and I'm still several months away from needing another fret job on that guitar), but this information does spark some idle curiosity: assuming that the current version (FG-700) is essentially the same as what I've got (FG-331), I wonder whether I would like a new one as much as I do the one that has aged in already. Wooden instruments do change their tone over time, and apparently how you play them affects just how the tone changes. Since I've been playing this axe for the whole twenty six years, the changes have been gradual and hard for me to notice; a side-by-side comparison between a new one and mine would probably be educational. But of course, I don't know for sure that the current ones are similar enough for the test to be meaningful if I were to walk into a store next week to try one out. (And also, when I get mine working again, it'll sound a little different -- possibly significantly different based on what the technician said -- from how it sounded the week before last.)
Unsurprisingly,
maugorn was right -- there are
a womdigious number of Yamaha FG-series guitars out in
the world. The line was introduced in the 1970s.
Eventually, I'd like to get my hands on an FG-100 (or whatever the current-production equivalent is). I don't like it as much as the FG-331 (or the FG-312) in general, but it's got a sound that'd be better for some pieces and would be a very useful tool for recording lead parts.
Alrighty then -- back to the sanding and filing. And wrinkling my nose at the scent of bone dust.