Have you ever made a quilt using 100% poly batting? If you have prewashed and preshrunk everything but the batting and you still get puckering, then it seems to me like it might be the batting. If I were you, I would do an experiment and make 2 practice sandwiches using white or light fabric on both sides. I'd prewash to preshrink the fabric and put poly batting in one, and cotton in the other. Quilt and bind, and after that I would carefully draw a 1" grid on it with permanent marker, so I can measure it after. Wash the way you'd normally wash a quilt and remeasure. If only the cotton one has puckers, there's your answer. If both do, inconclusive results, and we need more research.
I have some 1" grid sew in interfacing that might make a useful test subject for this, as I don't think it would shrink at all. I'd be more concerned that it fell apart.