What you listed are definitely the most common ways to thicken a sauce and most chefs stick to these basics.
However there ways I can think of to thicken sauce that you haven't mentioned.
Some chef use blended cooked vegetables as bases for sauces(carrot, cauliflower, etc). I don't see why it can't work the other way if it is a flavour that works well with your current sauce then the blended vegetables can be added in to thicken that sauce.
Gelatin found in roast liquids used to make gravies also participate in making the gravy thicker. I wouldn't recommend using powered gelatin though. You'll most likely end up putting too much and turn your sauce into savory jello. (Hmmmm lol)
Xanthan gum as derobert mention in his comment can also be used to thicken sauces. It is a type of natural corn sugar polysaccharide. However note that it is safe to ingest up to 15 grams per day. Eating too much of it will cause bloating and gas.