Which thickeners work well with dairy?
Your answer of "everything except arrowroot" is spot on. You should use a corn starch slurry in all likelihood. It is less expensive and more commonly available and will not create a "slimy" consistency; corn starch is also purported to have a creamier texture.

Arrow root also may have been overcooked by your preparation as described in your comment as it has a lower temperature that it needs to reach relative to other thickeners. Keep it handy for your acidic sauces, but keep to corn starch for the dairy. A benefit of arrowroot in clear sauces is that it won't make the sauce cloudy as will corn starch; however with dairy this is not a concern.