I think thats a good idea Mike. I would go to an Auto Upholstry shop and get some similar carpet in bulk make patterns out of your houndstooth mat and cardboard... then just cut them out. I would them see if I could get the shop to stitch a seam around the edge so it would look nice... a couple of small strips of velcro and there you go!
Using glue to hold all that carpet, IMO, is not a good idea...
Looks like I will be selling my Houndstooth Repro Mat soon!!.. I love this board!