The easiest way is to use a chemical clean. The disadvantage is that you really need to practice with an old reel to make sure the outcome is what you are looking for. Abrasive cleaners don't tend to give you a natural looking finish. Aluminum naturally oxidizes and if you used something that removes that oxide then the aluminum is even more prone to fingerprints etc as it reoxidizes. For an over the counter cleaner you might try the automotive stores as they have a number of products for cleaning aluminum wheels of dirt and grime without damaging the wheels. As with any restoration project, the project may wind up being much larger than you had planned. If I only needed 1 really nice reel I would be tempted to buy a new one and be done with it. If you don't have a lot invested in the old Goldbergs then you can try cleaning them up.
..Doyle
..Doyle