A smart solution. This is an on going problem for a lot of people and this may be a helpful way that works.
Something else that I learned to do years ago was to make a release cut, about 1/2" to an 1" long at the far end of the cut you want to make before you do the full cut. The fabric doesn't shift at the end of the cut when I do this and it is my routine method of cutting now. I can cut double folded fabric or one piece and it never shifts.
peace