After defeating Troya Ajak in the new Spirit of Vengeance flashpoint, travelling across the tether, and watching the small cutscene of Jekiah Ordo retreating to the bridge, I was warped back to Troya Ajak's area with no way to progress. There is nothing to click, and nowhere to go. Please tell me I don't have to exit this long and tedious flashpoint and restart it.

Just reiterating this point. You won't be able to skip right to WH.