For many people, doodling is not incompatible with paying attention. I actually focus very keenly on auditory input while doodling, more than I would if simply sitting there and looking around.
I was just doing a quilt with a lot of spiraling last night. One thing I noticed helps is to have a couple of other mini-motifs that you work in throughout the quilt to save you from awkward spots or blank areas. For me, often that will be a little paisley, or a smaller version of the spiral, or a heart -- whatever. As long as you repeat it randomly around your quilt a few times, it looks intentional.