Follow-up. My Harmony guitar is with the luthier now. He can fix it with hide glue and mahogany dust. I posed the question to him about a travel guitar, and whether to subject the battered Harmony to airplanes again. He recommended a baby Taylor over the Martin travel guitar, but recommended a 3/4 size Harmony or some such over that. He'll bring me a 3/4 guitar to try when I go to get my own back -- he has some he know longer needs to keep.
We agree that my own Harmony, made of mahogany, is better than anything else I could get now.
Thanks, everyone, for your help and suggestions.