Another great material for doing this type of thing is felt. You can get it for cheap, and almost everything stitches out beautifully on felt. Being non-woven and not a knit, it doesn't stretch, and yet it is thick enough that it isn't "see through" like just stabilizer or interfacing can be.
I must try just using the stabiliser, sounds like a good idea, I'm guessing tearaway is out of the question though, it would have to be permanent. Hugs and a flower for you dlmds.
ruthie, I use an iron on interfacing then the stabilizer also. Hugs and flowers for all.