Contact adhesive is always a good bet for foam. 3M make a bunch of spray versions like super 77. I'm not sure exactly what you're wanting but doing a little stitching will make the join infinitely more robust. mechanical bond > chemical bond
Your half right Nick, you sew the straps or elastic to a piece of fabric that's larger then the strap and Glue that piece with Barge or Spray 90 should be stronger.