Flying with a gun is no big deal IF the gun is legal in the state where the airport is located (I've heard horror stories out of NYC and Newark). Basically, you go to the counter, declare the gun and have it in a locked case, ammo stored seperately, they give you a tag and you're good to go. As an added bonus, your luggage will be the first off the plane as the security guys will hand deliver it.
OTOH, UPS will ship no problem. Locally, the UPS store won't handle guns, you have to take it to the local hub (why, I don't know, its just their policy here). Still, given that airlines charge extra for checked bags, shipping might be cheaper. I'd leave the AR and take a Glock. Just keep it unloaded and boxed in states where your CCW isn't honored, unless you're in your hotel room. As for mag capacity issues I don't know the answer to that one. Have fun though, and don't sweat it. The McClure Volkmer Act says that if the gun is legal in the state where you started and in your destination, its legal in transit. This does not include CCW, and having it ready to hand in a vehicle might qualify. But in the trunk etc. it shouldn't be an issue.
PS As to cases. You can get a Doskosil hard plastic case for under $20 at Wally World or Cabelas etc. You'll need to buy locks, but it pased muster. Of course this was pre-9/11 so God knows now, but they're solid cases for the money.