Waterworks

Another possible solution, with WAY more lights active. Just trying to get as *few* door nodes open as possible. 
Heck, you could just NOT use the far left 2 long piece, and make DoorR only have ONE active node. 

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Spoiler

Phobia begins removing connectors from the board. Immediately, things start powering down.




With all of the pieces disconnected (except the brake, no way she's touching that), the elevator is stopped and the lights are off.




Phobia then snaps the pieces back according to the new configuration.




The elevator powers back up, even better than before - You're moving up at a faster pace and the lights are no longer flickering! But what about the doors?




Philia goes to the leftmost door and is able to push it open without any resistance.




Phobia was able to not only able to power down the doors, she also made the other parts of the elevator work better than before! You tell her that you knew you could count on her.




With the doors open, you can just empty your entire tank out into the void below.




...Which you do. Right away.




All of your problems have been solved for the short-term! Now you can stay with Connie for as long as you need to, dumping any excess goo down the elevator shaft. However, you're not sure what you're going to do once you get to the top. You can't just leave her, and the shaft is the only safe place to dump the goo...