I don't know the exact compression strength or exactly how thin it should be, but here's my take on it.
ERC works well with a soft backing such as sinew, rawhide, fiber backings of those kinds because it is soft (and relatively low compression strength). If you are going to back it with wood, you are going to have to make it nice and thin; I would try to get it about 1/8". Doing it just right would require more precise methods than mine, but I think you would be fine with that.
Sean