Just realized op said “table” as I was wondering what this was going to be. I visualize 3 pieces, the bottom, the piece you show ( mid section) and a top.
For the bottom, I would use a quality 3/4 ply and cut it to the size of the od of the mid section. Cut a rabbet into the bottom outside edge for the mid section to fit into and band the exposed edge of the ply. Invert it and attach the ply bottom in several locations to the mid section pieces. You didn’t mention what the top will be made of.
If your slatted oval is the base, I think I would build a simple structure to fit loosely inside it and support the top. If the top isn't attached directly to that unusual base, there is no need to worry about movement between tge two. The hidden support structure can be a more traditional set of legs & aprons, or a trestle. Use standard table top attachment methods.