Keys get lost, cards get re-used indefinitely, passwords are a joke
So there is only one solution : neck collars. Personnel gets to the hospital, is intercepted by security team, gets wrestled to the ground and officer slaps neck collar on. Personnel is then free to go wherever and touch whatever computer, the neck collar automatically grants access. Collar stays on until personnel contract is terminated, HR in charge of retrieving it when processing the departure.
For bonus points, make the collar a nice one, so that the ladies actually don't mind wearing it and the men look more manly with it.