John,
I always use split pigskins as its very lightweight. The thicker the material the more hassle it is getting the glue to hold. I use contact cement to attach the neoprene pad, then the same to attach the pad, then stitch. I ordered a large quantity of the neoprene and would be happy to send you a small piece to try. After its stitched I go back and trim the excess material close to the stitching. I mark the stitch line and use my awl to mark the bottom corners and top of the arc to locate the pad, which is only slightly smaller than the area.
Hope this helps!
-Robert