Some ideas from someone who has never-ever used a soft backing:
Some of the parts houses (NAPA, Oreillys, Autozone- whatever you have in your area) sometimes have pads on the parts counter- with a slick plastic top over a dense foam pad. Maybe you could get them to donate their old ones instead of throwing them away? Seems they were kind of similar to the old mouse-pads.
Some high-dollar carpet pad is a fairly dense foam rubber- and how about the liner that goes down before laminate flooring?
My wife has a fancy little pad on the floor in front of the kitchen sink- like throw-rug, but it's 9/16" foam rubber with a skin on top- complete with rooster pictures!
Fred's felt suggestion is probably the best, but thought I'd throw out a few ideas, anyway.
I'm wondering- for what work do you guys find the soft backing most useful? Is it kind of in between using a flat platten and a slack belt?
Edit- Rudy posted while I was writing- and answered part of my question (thx).