I agree with the thrust of your post here--that anarchism has become excessively "jargonized"--but I take issue with your assertion that, "When you are an anarchist and you want little or no government, what you are saying in the United States is: you want the free market and you want that market based on supply and demand."
I believe this is a fallacy, or at least a misleading characterization of the type of economic system an anarchist (not anarcho-capitalist) desires. To speak with more honesty to the dominant schools of thought within anarchism, and to do my best at avoiding jargon the same as you do, I would rewrite it as follows:
"When you are an anarchist and you want [no] government, what you are saying in the United States is: you don't want laws that establish the production of necessary goods--food, clothes, medicine, etc.--as assets of an individual's property."
RE: Anarchy - How to Succeed - Translate Jargon 1