The repair in progress

I'd dampened the splintered wood and, from inside, pressed it back into place as best I could. Then I made a little patch from mahogany veneer, bigger than the break, and soaked it so that it would bend readily. This was glued in place -- on the inside -- using hide glue (so I could undo it if it didn't work) and held it in place with a five-pound bag of BBs, themselves held in place by powerful rare-earth magnets on the outside of the instrument. I let it sit for a week. Then I sanded it flush.