heres how id play it.
fill your carry on with your gear, like ya already said. ya have to have the gun in its case, so there goes one bag. in the other, bullets and clothes.

when your done, buy a cooler out west, have your buddy freeze your cape and mail it to you. it will be fine. or do the opposite and take your frozen stuff in the cooler on the plane and mail your clothes home. easy and cheap.