Yep. I think most of the two sided tapes I have seen would stick way too good.
No one has tried this yet to the best of my knowledge. But and this is a big BUT I have had in m head for a while.
If you glued the laminate to a sheet of thin sheet steel. Masking frames could be slapped on and off that had magnets built into the backs. Actually the whole backing wouldn't have to be steel just the areas where you would have the magnets located for the pieces you would change out. Might be as small as a couple 4 square pieces of sheet steel glued into pockets routed into a sheet of MDF.
I'm not real into masking or I would have tried something like this but if anyone wants to run with the idea feel free to show us the way. And if someone has tried it jump in and show us what you did.