I've never heard that you can't check your luggage prior to -2 hours and, most importantly, this is not written anywhere in A3's site. Unless this is a new, security-dictated measure that I'm not aware of, it does sound odd. From my personal experience I can say that I've checked my luggage several times at times between -3 and -4 hours (but not at -12 like you plan).

Since you have so much time available, and I have never, ever seen anybody at the transfer desk, I'd suggest to go up to the regular CI desks immediately after your arrival and the retrieval of your stuff, and see whether the agent at the M+B Gold dedicated desk would not be convinced to accept your luggage for your next flight. I'm almost certain that they'll say yes, especially if you look tired and tell them that you flew in from the US. Of course, if the (new) rule is that strict, well, go back to the arrivals floor and leave your stuff at the storage facility. When coming back in the evening leave your stuff at the storage facility until -2 hours, and do visit the A3 or the LH lounge. As NWIFlyer already wrote, you'll have to tell the person checking the BCs that you're visiting the A3 lounge. This should not be a problem, and you won't have to show your passport to anybody.