Upload & Sell: On
Can't tell for sure, but the OP pic looks like a sheet of luan (1/8" plywood) mounted to a frame. This is essentially how hollow core doors are made ... just that you only are making one face. Thinking the frame might be 1x3 sticks with the reinforcing braces.
If you made a wall that was (top & bottom) hinged or stacked, it could break down for storage. The obvious objection to that would be the "joint line". But, if your wall was intentionally designed as one with either a "chair rail" or wainscoting, the seam/joint could be hidden. You could use bead board on a frame (as above) for the bottom and your painted foam on a frame for the top.
You could even have multiple bottom halves, i.e. bead board, brick, stone, etc. to change things up. Might not be the solid color wall, but it could aid with your portability/break down/storage goals. I suppose you could also do painted foam on the bottom to give you multiple color options (chair rail to separate color / hide joint).