"Soft Jaws" are made from Brass, Aluminum, Copper, etec. And from heavy skirting leather. Haunt the junk yards for the metal, and flea markets for the leather. If you have any kind of leather shop around, or harness shop, that caters to the horse owners, you can usually find scraps of heavy leather there. Talk to stable owners, as to where they get their leather gear. I am near some Amish wagon builders, and I can always find heavy leather skirting at those shops. We used to have a Tandy Leather store here, but it closed and the closest one is now in Springfield, Illinois. That is 90 miles from here, but if I have to go to the State Capitol for another reason, I stop at Tandy's and stock up on what I need. Check the Tandy website to locate an outlet nearest to you.
There was a time when older industries still used long heavy leather belts to drive their machines. My father got some ends cut off the belts when they were fitted to the equipment out of the scrapheap, before they were thrown out as garbage, and we used that leather for projects for years.
And, there are mail order leather companies, where you can order any thickness of leather you want. I bought a bag of leather scraps from one such outfit for a few dollars and still have odds and ends to use for small projects.
Hint: For those looking for thin leather to use to wrap their flints, check out the Goodwill and Salvation army stores for old men's shoes. The tongues from the shoes, or even old wallets(purses) are perfect for this kind of thing, and will only set you back a dollar or less.
