This means that a paper tiger or and scorer is out of the question. Too much water or steam or solutions will cause both to come off.
So, since you want the bottom layer, you will have to pick and peel as you are doing. I do hope that this works for you, because I am afraid that somewhere down the line you will remove the top skin of the second layer and just rain on your parade.
be careful and when its tough, add more water to the surface.