I would avoid layers simply because it is inflexible, as it requires manual creation of the layers and can't be done at runtime, as well as not scaling well for larger puzzles.
I'm not sure if 36 layers would have any performance issues, but I suspect it might, since (I think) force own texture will draw each layer individually, and drawing your entire screen 36 times over every tick sounds like it might run into fill rate issues. The more layers you have the problem will only get worse, so again it is inflexible and unscalable.
As will all performance issues, try it out yourself and test if it is acceptable on your target platform.