Up at 3 am this morning and couldn't sleep so I doodled out an idea for a serving tray based on one from the mid-50s.
The bottom of the tray is two pieces of wood with a narrow space between them. I'm not sure how the thin pieces are attached to the ends on the original but I think the bottom pieces are probably quarter sawn so there'd be little or no movement. Maybe glue would be adequate.
One can buy the original for $325 or so.