I've done a bit of noodling online and the product offering is much more extensive than I would have thought. Thicknesses can be had from 1/8" to 1" or so. Several types of rubber are available: EPDM, Natural Gum, Neoprene, Nitrile, Recycled, Silicone, others? Apparently this stuff is popular for gym/exercise room flooring. I also found two retailers within 2 miles of me that sell rubber flooring.
I wonder if there are any problems associated with having a compressible material between my presses and bench top.