I am definitely NOT knowledgeable on AR coatings, so take this with a huge grain of salt, but I had a conversation with a Rolex trained watchmaker this evening as to what precautions there are regarding what I can or cannot use to clean the gen GMTIIC crystal? Specifically, I asked if Rolex had issued any warnings against the use of ammoniated cleaners like Windex (with ammonia) in regards to the GMTIIC's bezel or crystal. None that he was aware of. And he went at a GMT in the store with a bottle of Windex without any ill effects.
This is interesting because AR-treated CRT monitors or eyeglasses always come with explicit warnings NOT to use Windex or other cleaners containing ammonia, because the ammonia removes the AR coating. And I know it does, at least in the case of CRT monitors & eyeglasses, because I have damaged a couple monitors & an expensive pair of sunglasses (& I received quite a hefty bill from my optician to have the lenses redone).
Whether the AR used on Rolex cyclops is different than the AR used on CRTs & eyeglass lenses is different, I cannot say. But it does make me wonder if there may be something else going on?