Well, no, you can't legally buy a handgun if you're not a state resident. There may be some technicality that permits it, but ...
Flying is not really a hassle. I flew from Virginia to TX last week with my handgun, and had more issue with the suitcase being 2 lbs over the limit than with the firearm being in it.
Check out
http://www.carryconcealed.net/packngo. It's a handy tool to bookmark. You insert your permit(s) and the states you will travel through, and it will present much the same type of analysis you did for your trip.
Ain't it interesting that Maine recognizes so few other permits? My daughter got married there a few weeks ago, and I didn't get my permit application in in time, so it was go unarmed or OC. OC laws are odd, too - like having to unload when you get in a car - so the trip was much more of a headache than it could have been.