I can't see a way to make it work either. The best I have at the moment is:
[(A2 A6 v B1 B4)] [(A8 A5 v B3 B7)] [(A3 A7 v B8 B5)] [(A1 A4 v B2 B6)]
[(A1 A5 v B7 B2)] [(A2 A7 v B5 B1)] [(A8 A4 v B6 B3)] [(A3 A6 v B4 B8)]
[(A3 A4 v B5 B2)] [(A1 A7 v B6 B8)] [(A8 A6 v B7 B1)] [(A2 A5 v B4 B3)]
[(A2 A8 v B6 B5)] [(A1 A3 v B4 B7)] [(A5 A6 v B8 B2)] [(A7 A4 v B3 B1)]
[(A7 A6 v B2 B3)] [(A5 A4 v B1 B8)] [(A1 A8 v B5 B4)] [(A2 A3 v B7 B6)]
[(A2 A4 v B8 B7)] [(A1 A6 v B3 B5)] [(A3 A5 v B1 B6)] [(A8 A7 v B2 B4)]
which meets the 6 out of 7 teammates criterion. However everyone has one player on the opposite team who they never play against. Is that an improvement on what you have already?