You want to trim out any foam in the seam allowance.
You can still glue down the foam onto the (wrong side) of the fabric.
Cut the top fabric 1 inch larger, turn under 1/2 inch for the seam allowance.
Layer the two pieces together. Add glue or clips to hold together and then top stitch around the pieces.
You can even quilt a piece of batting onto the top fabric and then layer everything.
Trim out any batting in the seam allowance to eliminate bulk.
It sounds like a fun project!