I am making a quilt where all the blocks have very dense thick satin stitch applique plus machine embroidery stitches. Starch your fabric, use very,very firm wash away stabilizer or a strong paper behind your stitching. I find the stabilizer works a bit better while the paper is of course a lot cheaper. You are trying to get the fabric so strong that it won't be possible to pucker - about the strength of denim. Since you're using cotton, you have to get the strength from a combination of starch and backing. Using temporary spray adhesive to keep the paper on the back of your fabric is a trick that many use but it isn't truly frugal - works great though. Your block is fantastic!