There's still the problem of the fact that so long as the rest of the world doesn't ban spirits, smuggling is going to be extremely lucrative for organised crime.
This is especially a problem because the upper classes didn't violate Prohibition for beer, or even so much wine- they did it for spirits. This the great age of the cocktail! Smuggling whiskey in across the Canadian prairie or via St Pierre et Miquelon, or running rum across the Caribbean is going to be extremely good business. That in turn will- as per our timeline- incentivize any entrepreneurial American to start a still.
What are you going to do, raid your congressman's campaign party to see if they and all their donors are only drinking iced tea?