I used some VERY stiff ticking. I had first purchased some ticking, but it was the type you put on pillows. Had the very same problems as you did. Too stretchy. It twisted and turned on the roller. I tossed that out, as it would NEVER work.
Back to the fabric store - I purchased this VERY stiff ticking, which works lovely. I sewed a very long zip to it and attached the leader to the roller with self adhesive velcro. Works well.