The back side of the Masonite was framed like picture frame matting with 2 1/2" strips of 1/4" multi-ply plywood.
The contribution above was an attempt to show the slot idea. Photos above were for a traveling module.
There was also a sturdy corner brace to retain an even curve, otherwise the curve tends to flair out at the top on module mounted curved corners:
For Mianne bench work you could fashion a filler insert panel to provide a flush flat background mounting surface.