If I was making it, I would cut ribs out of plywood. Then cover the ribs with either bender board or 3-4 layers of 1/8" ply. I would cut the tops out of solid blocks and mount them on the 2 ends, then I would veneer the sides first, next the top and bottom. I would use 2 ply veneer. (Veneer with a wood back)

Figuring out how to do something you have never done is what makes a good challenge.