Thank you for this useful post.
From the image of the panel on Sear’s parts page (OP’s link) you can see the location of the one screw that holds the panel in place. The panel has tabs that slide in then down. To get to that screw remove the vent/filter trim piece on the top. The one screw keeps it from being bumped up and off. Beware of the wires. There’s not much room to work. I took the bottom trim off but maybe that wasn’t necessary. I’m trying super-glue in three points. Looks like original installation was glue on the heads of three screws then pressed into place. If my effort at super-glue fails I’ll try using a small block of wood behind the switch plate to wedge it in.