Going back over the second layer with a more careful eye to detail turns up a few cool things. First of, look at the seriously 'make-do' piecing in this light square. There are FOUR tiny strips of cream fabric, and one tiny square of pink, maybe 1/4" square. This says to me that the white was scrap fabric from another project, or the tad ends of rows of full squares. The print fabric would have been much more expensive, so that makes sense. The white swirl on the blue triangle is one of the cotton ties.
Here's clear evidence that this layer came from a bigger quilt - see how jagged that edge is, how the triangles don't finish, and how there's a remnant of the next square? At one point in time, this quilt was bigger than the 4-patch that eventually covered it. The rough edge was folded over smoothly, then the 4-patch was machine stitched to it.
At least some of the squares were once printed - if you look closely, I hope you can see the pale beige patterning on this one. I'm trying to find a place where I can get at the seam allowance without undoing any of the quilting.
And now back to the left hand side, with it's 20 inches of disappearing print and grid quilting. Putting everything else together, especially the fact that this quilt used to be bigger and was well worn before it became the batting and backing of the 4-patch, I think what we're looking at is a quilt for a four-poster bed, circa 1820-1840. These often had wide bands of contrasting fabric on the sides and bottom of the pieced portion, which generally covered the exact top of the bed. So at this point, I'm pretty sure the bottom layer is a pre-Civil War quilt. As such, it's fairly unusual, and I'll be taking it over to the local textile museum to learn more. I'll let you know if there's anything more to know, and thanks for all the warm interest and kind replies.