[...] just use a 4U gouge on the back side of the material. [...] and end up removing half the thickness.

Or you can go the easy way and use plumbers gasket. You knife carvers would be happy because you can carve all of the way through, as long as you keep it all connected. You can always glue it to a piece of cardstock to keep it all together.

The stuff I bought locally is thinner than the one above, but I didn't find it on their web site. There's always this that is 1/16" thick. Once you carve your stamp glue it to another piece of the same stuff to hold it together.

How does it carve? Is it smelly? I like this idea.

How does it carve? Is it smelly? I like this idea.

I bought some but I haven't carved it yet. We'll have to wait for someone who has to comment.