Is the basement ceiling finished? If it isn't, I would see if you could put up a long piece of pipe attached to the beams on both ends as close to the wall as you can. Get those cute little curtain hangers from Walmart that have the little teeth clothespins for hanging curtains. I clipped up a flannel backed tablecloth to those. You can then pull the tablecloth across the pipe and use the flannel back as a design wall. Blocks will stick quite well to it. I find for a quilt top that I need pins along the top to hold it.
If the ceiling is finished, you may need to get some cement screws with the anchors (if your husband doesn't mind holes in the wall) and fasten up something. OR Have you looked into the peel and stick cork squares? How about those interlocking foam mats you can buy at Walmart? They could be stuck to the wall with cement epoxy? Just a few things to think about, maybe someone else will have some more ideas for you.