It turns out that Apple's Migration Assistant ALSO breaks fonts!
After migrating, Hex Fiend started crashing on launch... And when I downloaded the source and ran it through gdb, I noticed it was crashing because it couldn't load a font.
So I downloaded the font again and double-clicked it to install it... But, nope -- Font Book started crashing too! Hurra!
Even the font selection dialog (apple-t) was crashing! Hurra for error checking!
Anyway, it turns out that the culprit lay in ~/Library/FontCollections -- all my old font collections, which (for whatever reason) make my new laptop very unhappy.
After cleaning out those, though, everything seems to be happy... For now...