How about using a travel agent? Maybe Amex. Should be much easier to get through to someone.
For me, the bigger issue seems to be that the AF website is no longer offering the "next higher" class in the search results column. In the past, if I searched for business class, it would show results for Business class and, in the next column, La Premiere. That would let me do a mixed-class booking (e.g. business on the eastbound TATL redeye, first on the return). I don't know any other way to do that (other than via phone).