Hi Phil,  The rear panel on my Olympia/Criterion 20.5-inch upright is
about 3/8-inch thick and acts as the sound board.  The panel has two
1"x3/4" pieces of wood glued to it that contact the bed plate.  The
wood appears to be pine or spruce and is glued together to form one
panel and is fastened to the case perimeter with wood screws.  Maybe
this will help, I hope so.

Regards,
Jim Morgan