I would do a line of machine stitching on the top only, all around, just a tad bit smaller than my scant 1/4, then I'd go ahead and make my sandwhich.
I would worry that if I stitched all 3 layers together, then I would end up with puff somewhere that I didn't want it in the center!
No matter what you do, I think the consensus on here is to stitch your edges first. Good Luck!