I've pre-soaked Warm & Natural batting for shrinkage and still had a crinkle effect after machine washing and drying. Probably the best way to avoid any crinkle would be to (cautiously, as wet bats can be pretty fragile) pre-soak whatever bat you use and then wash the quilt in cold water and dry flat rather than drying with heat. In her Heirloom Machine Quilting book, Harriet Hargrave recommended drying by laying the washed quilt outside on some bushes where the weight is supported. I would try this if I had any bushes! I imagine a quilt takes a long time to dry on the floor (with something plastic underneath to protect the floor), but I've read that setting up some fans in the room helps hasten the process.
Maybe someone who has compared the two can say whether the 80/20 mix shrinks less than the 100% cotton bats, with or without pre-soaking.