I like the idea of muslin as a 'backing' for each piece of the pillow. I would probably sew the squares together for a front piece, then back it with muslin. Then sew the squares together for a back piece, then back that with muslin. I think for good measure I would sew a few lines through it (like quilting it). I don't think it would have to be that dense (maybe a three or four vertical and a couple horizontal???) but that would prevent the whole thing from bunching up inside. It's more like you are making an 'interlining'.
Then after that I would sew the front & back pieces together with French seams and then apply the band.
I'm sure they will be beautiful!