The idea is really neat and I would have liked to see more focus on the design and balance. I found the best strategy is to repeatedly spam one dialogue that works on all followers, not even bother with the other options, and make it to the gate on time. Possibly spam it near the gate just enough so you can go get the lever and get back.
To sum it up, it's a fun concept, but falls short because of the design. That said, it looks very promising and I would have liked to see it fleshed out more.