Here is half, (maybe a quarter) of one. It’s not as extreme as your build, but basically the same technique. If it were me I would apply the ring shaped veneer to the sides before veneering the top and bottom.
It looks like the top and bottom are flat to me. I think the taper is making it look compounded.
I’ll be glad to help what I can, but I’m just an ole butch carpenter using contact cement and a block of wood to press it.
Figuring out how to do something you have never done is what makes a good challenge.