There is no reason to have a timed experience for this game. It takes away from the overall feel of the game and adds nothing. I doubt the developer make money off of the timer any way as there is other content to pay for which is more valuable than a one time boost.
Just make elevator shaft go up 7 floors and over lap on a floor with service between. Then use staff elevators. Elevators only stop well at the top and bottom floors use that.
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