I did speak to Southwest twice. I got different information each time, but their (vague) written policy and the more knowledgeable-seeming answer was that a cello can’t have a seat and must be checked. I haven’t gotten through to American, but I’ve reached out to a couple of friends who work for them.
If son does end up attending a distant school for cello (he’s also auditioning on voice) we will have to work through the logistics. Just for the auditions (he only has two that are further than a drive) I thought we could just book a seat, but it’s not so simple as it seemed. I haven’t looked into finding a travel case but that may turn out to be the best option in the end.