I am of the opinion that there is no reason NOT to use the knits/double knits/polyesters. In fact in some ways they are actually to be preferred because of ease of care and durability factors. Just use them in separate quilts. That is make ones that are all double knit, ones that are all polyester prints/solids, ones that are all home decor fabric and ones that are all cottons.
If I were doing it, I would also try to come up with aesthetically pleasing combinations of fabrics in each quilt and of course be sure they are well made and will hold up to hard usage.
Good luck and I hope everyone in your group will get on board with this project.