What do you do with the steam battery on steamworks island?

The Steam Battery lets you open the two doors (Sully, Living Quarters) and lower the Bridge. But you need a separate key for each. Sully's is inside the robot crab at the Living Quarters door (jump on him), the Bridge key is in Captain Ziggs room at the Hub, and the Living Quarters key is way, way across the game in the laboratory at far right of the island, across the bridge.

(see the related question below)