I find I have some pieced tops that don't quite lay flat. This all gets worked out when the pieced top turns into a quilt. Adding the batting and backing and then washing lets everything play nicely together. Plus any imperfections in the piecing gets worked out as you quilt.
If you look at coverlets or bedspreads, one of the key things is that there aren't very many seams. The other thing is that a lot of them have in common, is a webbing on the back of the top fabric. Technically they aren't quilted, but give the appearance of being a quilted top.
This is just my opinion....If I were doing what you are, I would buy "thin" flannel, wash it to make it go ahead and shrink and quilt the top with the flannel in the middle. That way there isn't a lot of bulk, it is lighter weight, and you will actually have a quilt rather than a pieced coverlet.
Good luck with your project, I will love seeing some pictures as you work on it.