As Scottiemom said, it would take a LOT of velcro. That was our first idea. But found it would cost a bunch. Didn't know if someone had found a different solution.
We have a Travasak (has a zipper problem) which has cotton sheets and the velcro on the sheets are the smooth part not the snaggy part of velcro. It sounds like the issue is that the snaggy part would not be a problem on cotton sheets. Not sure we want to go thru the challenge of removing the velcro from the Sleep System micro fiber sheets and putting it on some cotton sheets. Bummer. Guess its time to get the Travasak fixed.