If you eat non-grainy starches, you can use potato starch or potato flour, or rice flour if you eat rice (you'll have to cook out the flour a bit). Don't use tapioca, as it will make the sauce slimy. I have never tried coconut flour in sauces, but that might be an option as well, or you could use actual blended potato as a thickener, like in stews or soups.
I know some people who make "cream" soups by blending in some white rice, and that might work as well.
Another option is to leave out the starch altogether and make the sauce with cream that has been reduced (simmer over low heat so as not to scorch) and just add your cheese. Very thick and rich.