@ryanc I don't know with any confidence any specific adhesive but I suspect 3M has something that will adhere rubbery to plasticy surfaces - itches my brain that it would be an automotive body repair product. Mechanically my first inclination is (ab)using flooring transition strip as a screw-down clamp around the edges of the mat. No need to put holes in the mat, it's long-term but can be loosened and re-clamped in case the mat 'grows' with use or solvent exposure.