Choosing an elevator definitely enhanced the claustrophobic feel of your game and its narrative. Moreover, it juxtaposes very well with the No, I'm not a Human type of games where you are mechanically limited by your choices, but also visually!
During the talking events between the people that you let in, in order to increment the intensity of the atmosphere and to allow the player to have more control over the selection of people, maybe we could receive more clues from the anomalies we picked along the way. That way, if we found out we had an anomaly on board with us, but could not evacuate them until the very bottom, we would increase tension :)
Plus, your use of the count down works naturally well with the elevator, but it also adds mystery to what will happen at the end: the result of all your actions. Creating this want to continue playing.
And remembering a name reminded me of Potato man in Papers, Please! :D