This is the problem with any “dribble it out” scheme. Sooner or later, one bill will be noticed. That will cause the feds to descend on the area and demand every bank check every bill. More are discovered. Bit by bit, they narrow down which businesses. For some businesses, a person spending $20 with one bill would be notable, back when McD hamburgers were 35¢. It would be like someone cashing a $100 bill today. The only difference would be a lot less credit cards, but my experience with relatives in the USA back then was they wrote a helluva lot of cheques, not cash.
Then the question would be, was he just passing through or is a lot of the money being spent in the area? How wide a geographic area? I would avoid smaller rural areas, I imagine the feds would be scrutinizing all white males between certain ages, and their history in that area (any new arrivals?) so you want to choose a city of a million or more.
But then you have the issue that you need to pay rent. I don’t know what a common rent would be, but certainly some decent multiple of $20 - so some landlord is depositing a significant number of those marked bills every month, and when the banks become alert for the bills, that will be one of the first things that raises flags.
I think the simplest thing would be to go back to your regular drudge job, and spend the money slowly as far from home as possible. However, this bring to mind those stories about serial killers, and how the location distribution of their murders helps pinpoint their home base - if the feds are looking for bills and they pop up here and there, because you are driving long distances to buy that colour TV or fancy fishing rod or whatever else that you can spend but can’t be easily tracked back… sooner or later a pattern will emerge.