I was inspired by overcooked :D
Your idea for removing the elevator buttons is great, the should just go between their stations all the time, adds a timing skill to the whole game. I understand your concerns about the UI, but I like the idea of having to check from time to time, that one player needs to physically be in the correct place and could then communicate with the team. Something that gives feedback to the player like the dummy image would be great, but I am unsure what to do their.
All in all thank you for your detailed feedback. Have a nice day :D