On the subject of "keep the tank alive": As a WHM, you can toss anything without a cast time, such as Regen, on the Tank, while you're running.

Combined with Tint's suggestion to Sprint when the tank sprints, y'all should be okay -- unless you have one of those tanks that doesn't bother to mitigate dungeon trash, in which case, you're in for a rough time no matter what you do.