Oh rats!!! I figured you weren't being literal!
LOL..
Your story is a bit of a let down urban six, but I do wish you well in resolving your naked shovelglove problem!
I never liked using the sweater and just leave it uncovered.
The real spirit of Shovelglove is the great feeling of doing it!
So don't worry about the sweater

If you feel you need to pad it, I suggest taking a small hand towel, fold it, and then tape it with duct tape.
No, not as weird and geeky as a sweater, but would protect your floors!
Have a nice weekend

Peace,
Debs