I've used cut up PVC lattice to make strips. They are only about 1/4 high so catching wouldn't be a problem on the rivets.
However, I read here that the prohibition against using any kind of strip on riveted boats has more to do with the rivet, pressed on the hardened strip, putting excessive pressure on the rivet and the material surrounding the rivet. Makes sense to me. I woudn't use strips of any kind on a riveted boat.
Some guys us canning wax on their carpet. You can buy blocks of it and just rub it on AFTER you return from a trip, but prior to re-loading your boat. That way, the carpet has some time to sit in the sun, dry off, and be heated somewhat.
Certainly worth a try. Also, I don't see why any winch could not be turned around and, after reversing the strapping, work just fine. Never tried it...but??? have you tried that? Rich