Answer: Sax players have been using rubber patches to cushion their mouthpieces for years! Just ask for a mouthpiece patch at a music store or a woodwind-type supply house. You may have to trim it a bit for the EVI mouthpiece, but it should solve the problem. Put a patch on the replacement mouthpiece before you begin to use it so that you will be wearing out the patch not the mouthpiece.
Other items that work well are two layers of black electrical tape or rubber non-skid pads made for bath tubs.