Have the same problem.
Finished all quests for the Knights and the Dozen. Also i annihilated the Doemenel.
The Dozen dont want to give me their invitation because i helped the knights, and the knights dont want to give me their invitation because i helped the dozen :/
save:
https://drive.google.com/file/d/0B8eJLqXOxWmKbFo3M0VTdGQ0M0U/view?usp=sharing