Thanks Fender and Trevor. I have some Titebond (aliphatic resin) that I can try injecting, but I don't know if I can get much down there. I can't even fit a piece of paper into the crack.

Putting a dowel into the hole by the neck should lock down that section. For the rest, what if I drilled a few vertical holes along the crack and glued pieces of dowel into them? That should secure those places pretty well. And I could put one at the end to keep the crack from spreading.