The adds spawned during the fight by Endgineer Omegaplugg won't spawn if the activation conduits around the room are clicked in a specific order. There are 6 conduits in the room, from the left of the entrance of the Tinkers' Court all around to the right, we'll label that 1, 2, 3, 4, 5, and 6. To prevent the adds from spawning, try clicking the buttons on the sides of the conduits in the following order: 1, 2, 3, 5, 6, 4. Ideally, someone with high mobility should click conduit 4's button after conduit 6's button has been pressed. He will kill you, but once you return and pull the boss again the adds should no longer spawn.
From there, simply avoid mechanics and interrupt his repair ability that he does starting at 50%. Best of luck!