Sounds like a good idea.
A big dresden plate comes to mind -- just make the strata and cut. Your strata would need to be about 38" wide. I did a 60" Christmas Tree skirt without a slit (DDs orders) this way -- I cut varying width strips and used 2 different strata (I did not want to deal with matching seams so the width of strips was different for each strata). I would make the strips of the strata for a table cloth kind of wide so you can put glasses on it without wobbling on the seams.
I have not been able to find large round cotton table cloths, so if the back you use is polyester make sure to tell them to protect the table cloth when setting hot things on it. Warm and natural should work well for batting since it is all cotton it will work with hot things and it is pretty thin so you can set glasses on it.