Or if you have any Ailene's Tack It Over & Over glue, or Mono Multi in the green & white bottle, just spread that over the back of the stamp - over all the sticky foam and the label if you put one on. After the glue dries, stick the stamps to the back of your hand or your jeans a couple of times, and the stamps will work just like the EZ mount cling ones that you're used to.
It might even work to just stick the stamps on & off your hand or jeans the way they are now and that might reduce the stickiness enough that they'll work on the blocks, but I haven't tried that. I know the glue will work