You do not have to actually open every door by yourself. If there are still doors to open by the time you are ready to exit, just move the crystal. The remaining doors will begin to open as you leave so that the monsters can chase you. After moving the crystal, and you make it to the exit before all of the doors are open, wait a few seconds. A message will appear, stating that the last door of the floor has opened. When it does, use the exit.