I would first try to chemically clean the roof of your window. I used commercial cleaners like Tarn-x to remove the patina. I have also used a white vinegar and salt solution. Vinegar and salt works well on any kind of oxidation and can be used to force a patina, also.
I never bothered trying to remove pitting on outside copper trim on my house. I would just clean it and coat it with a clear coat or even linseed oil.