So I was pleasantly surprised to find that the set of velcro backed mats I received today have an improved stronger backing, instead of that flimsy foam stuff that rips on the original floor mats.
These are the floor mats with the "BMW" healpad on the drivers side mat, and attach using velcro, part number 82111470424.
FYI - Not to be confused with the "newer" style of floor mats that don't have the "BMW" healpad, and attach using clips instead of velcro, part number 51478201222.