Thanks for all the helpful suggestions. In the end, I wasn't able to find a direct replacement. V-brake boots don't fit at either end, and my local electrical supply shop didn't have anything (though maybe a better stocked one would?).

Shimano makes a Sealed Cap & Tongue & Rubber Shield that I thought might work:
And it very nearly did work too (if it weren't for those meddling kids . . .), but the boot was too big to fit through the opening in the flange for the original boot, which also doubled as the derailleur cable stop.
What I wound up doing was installing the Shimano sealed cap above the flange and then using a piece of heat-shrink tubing to seal around the joint between the cap and the flange. Time will tell whether it works, but in the meantime, I figure it's better than nothing and probably at least as good as the torn boot it's replacing.