So, you're mixing minky fleece and cotton blocks for your quilt?
Not an impossible task, but you would probably have better luck using a walking foot on your regular sewing machine. A walking foot would help to feed both layers together. Before you reassemble your entire quilt top, you may want to play with a few scraps using the walking foot to see if it feeds better with the cotton fabric on the top or the bottom. I don't use minky a lot because all of that fuzz makes me crazy, so I'm not sure which fabric will feed better on the top.