Gonna echo Frizze. While the scenario skip potions mark everything MSQ-related as complete, I don't think that the game itself counts the dungeons as "complete" in the same way they would be if one ran them through normally, because there have been instances where I've landed in HW leveling dungeons with a potion user, and they still receive the mapping achievements and a newbie bonus appears (and none of the other players have been new since they usually had multiple classes at level cap or close to it).

Would be worth trying out Garuda, Titan, and Ifrit HM (all of which can be easily unsynced with 2 or 3 people, if not just outright soloed), and see if running and completing the trials prompts Urianger to give you the Ex unlocks and Coil unlocks.