Hi Yvonne,
The simple answer is that you do not need a radius no matter the size of the guitar. The radius gives a little protection against drops in humidity causing cracks among other things, but you can easily build without a radius.
Second, that piece of walnut might be pretty, but it might also be unstable. If you sticker it, i.e. put it on two sticks of wood that run across the grain and elevate it off of the table, add two more sticks on top so they line up with the first two, then put weight on the whole thing, it might help. You want air to be able to flow over the top and bottom of the wood equally or the wood will lose or gain moisture from the air more quickly on the exposed side and cup, or turn into a manta ray as you put it.
If, after several days or longer(depending on how dry it was to begin with) of the wood being stickered like that, the wood continues to misbehave, you probably do not want to build with it. If it gets flat and stays flat without weight, but still stickered, you will probably be fine.
I hope this was helpful.
Tony