Remember that a purse doesn’t count against your “one carry on” item. So you can always find a big ugly one at goodwill and stuff it full of books and snacks.
I’ll still likely be one over the limit on the way back - I’m not taking my good guitar; I’m going to buy a cheapish-and-sturdy-but-good one from someone there. He’s a Vermonter I’ve met a number of times, so I trust him. Actually he and a handful of the other Vermonters on that list were the first internet folks I met in real life. We all got tickets to a concert and my dad and brother came, too. We guitar list folk started continuing with conversations that had started on-line...”how’s your cat doing? How do you like that new mandolin of yours? Did you see that discussion about...” Kinda freaked Dad out a bit, I think. ;-)
I think what I’ll do is just pay the $25 they charge for a second bag, and then gate check the guitar. It’d still be cheaper than mailing it insured. The tricky part is going to be gate checking, ‘cause I don’t know how to do it or where you go to pick the item up when you get there.