Some very constructive solutions offered here, I bet that was just what you were hoping for...
But hey, that's pretty standard for CGN
Anyway, no aftermarket parts that I'm aware of, but here's something approaching a mechanical fix. All modern 870 have an amazing number of sharp edges. These edges are more likely to grab at and catch the fabric on your gloves, loose fitting or not. You might reduce the problem by beveling and polishing some of the sharp edges: The lip and forward edges of the shell carrier, and inside the receiver, around and inside the forward portion of the mouth of the bottom port, and the lower circumference of mouth of the mag tube.
Worth a try.