Thanks for the tip. I've tried this technique with a heat gun with more or less success. When the foam started to curl I used a rolling pin to make it smooth again. Not ideal, as the foam distorts a bit, but if there's nothing else, it can be an option.

Funny thing is, the Woodware punches could easily handle cutting through the foam, if the slot where you slide in the sheet was a bit deeper. I guess, the manufacturers just didn't think of it.

I did find a "defective" sheet in a pack of Funky Foam, which was about half the thickness of the others, and it punched beautifully, so I know it would work if only I could find thinner foam. So far, I have been unsuccessful