lindaschipper, you didn't say why you don't do paper piecing. Is it just something you don't enjoy, or you haven't learned to yet, or you don't like the wasted fabric? I learned when doing the Harriet's Journey sew-along a couple of years ago, and it isn't hard at all, just different.
I don't think I'd try to traditionally piece the pickled peel quilt, but I might have a go at paper-piecing it.