Not all clear plastic is technically acetate, but the theory is that actual acetate will cause a reaction with the foam in EZ moun. From what I understand, that actually causes them to permanently fuse together. I haven't heard of it losing the sticky.
I am just now embarking on the journey of unmounting my stamps. I have three sets done, woo hoo! But clearly I am no expert. All I can tell you is that EZ Mount seemed expensive for my current budget. I liked the Tack and Peel idea and even purchased a few sheets but couldn't come up with a solution I liked for storing the (not sticky) stamps. I have see. Where people use the trading card style (9 pocket) binder inserts. One stamp goes in each along with a card stock index page so you can see the image. If you stamp an index shed you could also theoretically use a cd or DVD case and just let the stamps rattle around in there.
My current choice is to use Aleen's Tack It Over and Over. You do have to paint it on each stamp but it is not expensive and a little goes a long way. I personally add a drop or two of water to my glue and make sure I paint on a very thing layer - it seems to work so far. You could either strip yours down to pare rubber, try painting the glue over the existing EZ Mount, or stamp the image on tissue paper and put that between the foam and the glue.
Just remember to let it dry fully so it is clear and tacky before sticking the stamp to anything.
Sorry for the long post. You can also search here and google for unmounting techniques. Good luck!