When changing out rolls I was never able to get the used roll off with out unrolling it.
I have two 5000' running on my system. I agree it's tough to remove the used fleece/split sleeve from the takeup roller, but I have never had to unwind. Jut grip the used material firmly, holding it by the end of the roll of taken-up material closest to the mounting screw, and push from the other, open end of the takeup roller. You might need to use a dowel rod, though I've never not been able to push it out with steady finger pressure.