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The bit about rushing through before outleveling it, that is exactly what happened to my group too, and I never actually got a satisfying answer for myself either. What I can say is Hall of Thanes sits in that level 13-18 window beneath Ironforge, dealing with Dark Iron infiltrators and undead disturbing the dwarves' burial chamber, so there is at least a clear theme to the place even before anyone opens a quest book.
I have only ever gone in early myself, queued the moment I hit the range while still puttering around Ironforge doing my own thing, and honestly it felt complete as an experience, not like I was skipping some preamble. Whether waiting for a surrounding questline changes anything about the pacing or the pull order in a meaningful way, I genuinely do not know, I have not run it the patient way to compare, and I do not know enough about how quests there tie into the dungeon to say more than that.
Has anyone actually done both, waited it out fully versus just diving in, and noticed a real difference in how the chamber plays rather than just a difference in how rushed the group felt?