Cannot continue storyline

During the quest "Duty, Honor, Country" I entered the Heart of the Sworn by talking to a Sultansworn Elite. I finished the quest, at which point the next main story quest, "A Matter of Tradition" became available from Owyne. I exited the building without taking on the quest, went to the inn at the Ul'dah Adventurer's Guild and logged off.

When I logged back in I did a few sidequests and guildleves before I noticed that I could no longer access the next main story quest. It doesn't appear in my journal or my recommendations list and the Sultansworn Elite I spoke to earlier is now gone. I can't access the Heart of the Sworn and I'm completely locked out of the main questline as a result.