Do you think the fabrics would look good in a quilt? If so, use them that way, perhaps all together with no cotton fabrics added. You could also use them for curtains or even a quilted table topper. I like the idea of rope baskets or perhaps organizing baskets for holding stash.
As a side note, my first quilt, started in 1972 and finished in 1986, was all poly-cotton with poly batting and is still holding up well. It took a long time to hand quilt and later I discovered that hand quilting 100% cotton is a lot easier.