As I understand it —correct me if this is not what you intend— the finish you want is weathered aluminum. This is normally a flat light-gray or off-white metallic look. This is caused by 'deep' oxidation of the aluminum.
Aluminum always has an oxide layer, but on fresh cuts or new aluminum the oxide layer is all-but invisible. You could try adding some hydrogen peroxide from the drugstore into your existing weak lye solution. Another way is to simply put the aluminum sheets in some water outside and leave them in it a few weeks, moving them every so often to keep the oxidation even. If perfect authenticity is your goal, then chemically 'aging' the aluminum is what you have to do.
But . . . for a model it seems to me like you are trying to do this the hard way.
An airbrush —yours or a friends— with matte clearcoat and a touch of very light gray mixed in it would get the job done in a few minutes, and dry in an hour. The aluminum color and sheen would still show through, but have the added 'oxidation' from the paint.