I too put mine in with large frames. I bought large narrow boxes from U-Haul that are for pictures and mirrors. After I wrapped the pictures with blankets there was still a little bit of movement in the box so I just filled the box with fabric (on the side opposite the mats so that they stayed flat) until nothing moved in any direction. (You've got to put all that valuable fabric somewhere when you move!)
Here is the link to one that is 27 x 37.
https://www.uhaul.com/MovingSupplies...e-Box/?id=8697