I agree with ckcowl. I think a light batting to diffuse the seams would help. And a nice flannel backing. Since you've serged the piecing, I don't think you need to worry about raveling. Might want to serge around the outside edge just for kicks as long as it doesn't affect your pattern/block size. Otherwise maybe just a stay-stich seam around the outside edge if you're going to do a binding. I, too, think a binding would be far easier than a 'birthing' or 'pillowcase' method.