I was completing main story quests whilst registering for duty via the duty finder. When I was in the middle of the quest "Every Little Thing She Does Is Magitek" (specifically running the magitek to the destination after speaking with Wedge) my duty finder popped up and I accepted the duty. After the duty I was still on the quest but no longer on the magitek. I walked to the destination point and on approach was told that I "had lost maggie" and had to return to speak with Wedge. However there is no way to get back into the room with Wedge and therefore am unable to complete the quest.

I tried logging out and back in and with it being a main story quest was unable to abandon the quest to start again.