I collect vintage military firearms which can sometimes need some significant cleaner.
You are probably dealing with a combination of oxidation and crud.
Have you tried Simple Green? If that does not work, before going to an abrasive, I, myself, would try acetone. Be sure to do that away from flame and in plenty of ventilation.
Another chemical suggestion: there is, iirc, a variation of the rust-remover, Naval Jelly, which is made for aluminum.
Actually, come to think of it, I might try really hot water, a bristle brush, and Comet cleanser, but household cleansers can be pretty abrasive.
There is a very mild abrasive polish called Simachrome but it will be slow going.