I fly with Zam all over the country, a lot. Zero damage from travel so far, although I haven't popped the bin open since I got back yet. Anyway, I use a "JTL" trunk, it's on Amazon or in a container-carrying store, about 30 bucks. Smaller sized than a regular bin for TK, it can hold all my Zam armor, clothing, and a full Jedi cloak and repair kit (but not the helmet, that would crush it). It's airline-approved and counts as a regular piece of luggage (not oversize). It should say that in the product description. Wheeled, has a place to lock it with a TSA lock.
My only complaint about it is that the side handle that you use to haul it is not expandable, so it tugs on your arm a bit hauling it around. Also the weight limit on any piece of luggage on the airline is 50 pounds, watch out for that. (Weigh it before you go.)
My helmet for Zam is fiberglass with the binocs, and it goes in a polar fleece wrap and then in a motorcycle helmet bag, which goes either in my lap or as carry on under the seat in front of me.
I don't have the rifle yet, but I'm planning to make it break down into pieces that fit in the JTL trunk.
-Deunan Shiruba (Seattle Zam)
