Interesting Kevin, I wonder what that backing was? Near me (in Macon, Ga.) there is a discount store that sells Home Depot & Lowes leftovers, returns, discontinued stuff. They have tons (literally) of all sorts of floor & wall tiles, I think you could even buy just one piece if you wanted. You might check your area, or places that you travel to, for similar stores to check for "the good stuff".
Have you tried to do a mirror?