Whether he post or not, the table and benches in the room should be out of the way and the cart should be in the room by the time Zeke would have gone up to the turn in the corridor. Galdar is riding on the cart if he so chooses.
It only takes 2 of you to pull the cart, you could probably have a couple riding try and sneak in a cheeky short rest. Who knows how long this tunnel will take.