I have had the same issue where a good Corby press was suffering from the foam/nylon back pad failing disintegrating and sticky to the touch (yuck)!
I dismantled the top and bottom, removed the drop-down flap, removed (cleaned-off) the old material and replaced it usuing a new ironing board cover as the material, trimmed to size and stapled in place with a big upholsterer’s Stanley FatMax FMHTO 70868 staple gun (making sure to avoid the heating element). Looks fantastic.
dr tobin
June 2021