I purchased this vise and plan to remove and reinstall a barrel or two with it. I am wondering if I should find some thin leather to protect the barrel. I also saw recommendations of business cards, bike inner tube and toilet paper rolls. I would think leather would be the safest but may cause the barrel to slip?
21stcenturyinnovation.com
I was looking at this for leather, seems pretty thin.

1 5/8" Barrel Vise
Barrel Vise For barrel installation, removal & maintenance Precision cut v-shaped jaws accommodate barrels up to 1 5/8” Front-to-back play allows jaws to adapt to barrel taper—no bushings required Anodized aluminum won’t scratch or ding your barrel Shoot a rifle enough and the time will come...

I was looking at this for leather, seems pretty thin.