Paul,
When I ship larger ground screens, I make a crate out of 1x4 wood, and a piece of luan on each side stapled, then put a 2" piece of builders foam on one side and a 1.5 piece on the other side and encase the screen in cardboard, one side of the crate is luan 1/4" that is glued and stapled, and the other side is 1/4" luan that is screwed so they can remove it, I have shipped all the way up to 20x30 inch screens this way, with very few problems and the crates are reusable..they are a little more weight to ship, but help ensure your pictures will arrive at the next destination. My system is actually very simular to the way many museums ship pictures to each other. My largest crates run me about $20 in time and materials, and of course you could make our of 1 x 6, 1 x 8 depending on how many pictures you wish to ship in each crate. And do insure them for there worth, because even the most secure shipping crate can get damaged. I would not recommending switching to plexi, unless you are willing to spend the high dollars required to get good quality museum quality plexi for framing, and it ain't cheap..
Dave