If I ever do oxdising frames, I will scrub and scrub the top of the frames until I can no longer see milk running down the glass, if you are using a good flow rate and make sure you are thorough you can not go wrong. It will take longer, but I'd rather take twice as long on the first clean, than either make a mistake and look bad, or have to be extra careful every time I go back by making sure I don't touch the top of the frame.
Basically as long as you scrub and rinse for long enough, the oxidised layer will be removed (in my experience). Once the water is running clear again, go over it another couple of time to make sure.