I think there are actually two types of darkening that need to be removed from aluminum. The first is the traditional black, fat or oil based coating from just plain cooking. That's the one that lye takes off cast iron and electrolosis works well for on iron.
The other is a corrosion caused by a reaction between the aluminum and whatever has been cooked. Things with ammonia in them will cause this darkening. A weak acid solution (a couple tablespoons of cream of tartar in a gallon of water) removes this easily.
I don't know the acid that is in cream of tartar (other than it is tartaric acid). I think the acid in rhubarb is oxalic acid. I suspect that it works the same as cream of tartar because of this.
I haven't found a chemical cleaner that works easily, although I have used full strength cleaning ammonia to cut some grease. It turned the pan a nice even black that I was able to instantly turn back to normal with cream of tartar. Not for the faint of heart though.
A final buffing of the clean pan with 0000 steel wool really puts the polish back on without leaving visible scratches. I don't use a powered wire wheel, it does clean, but to me it leaves an unnatural polish that the hand work does not.
I prefer the self cleaning oven. If I can't remove non-aluminum parts (like a waffle iron with riveted on steel coil handles), I now use walnut shells in my sandblaster. Work like magic, but a big mess.
Tom
It will be interesting to follow the results of your test.