I'm confused. If the beer is in a mini fridge, then why would the copper inside it make a difference? I mean the copper will be at fridge temp, and so will the beer. In this case, a plastic hose would be better because as it exits the fridge, it will be better insulated from the 3 foot exposure to the tap on the bar.
Infact copper between the bar and fridge would be a way to level the temps between the bar air and the fridge air (ie conduction) and seems like a less energy efficent thing to do.
Edit:
rereading the OP, I see that the first 3 feet are too warm, which could be an entire glass I suppose. In that case, the aluminum should work, it is fairly conductive, although with less mass, it has less thermal mass to keep the beer cold. You might want to get the pipe insulation on whatever your solution is. (that black stuff) it is $$$ but again, it helps keep the cold and hot where they are supposed to be.