Hi, I have a set of near antique nesting tables with very thin tops, and tapered and turned legs that are quite beautiful and stable. There are 2 inch hardwood trusses (frames) on the back and two sides of each of these tables, with an open front for the next table to slide in. Those trusses will help prevent further twisting, especially at 5/8ths thickness.
You might also consider (after removing the twist, creating a second layer below to add strength and thickness, a less expensive piece of the same material could be used for this purpose. Attached is a picture of the tables I have (but in better condition). The legs are delicate, but you could simply use tapered legs. Or straight legs like the other example.
I'm posting this because your stock is really beautiful, and would be perfect for a more special looking set than what your original design shows And the techniques required are really not particularly more complicated. Of course you could use well concealed pocket screws and glue, which would simplify the construction.
The more I do, the less I accomplish.