It would be a great idea to have the hospital ending lead to a screen resembling the Game Crash screen, except the detail text describes what happened in-universe. The final message would say, "ERROR: HUMAN INTERFACE TERMINATED." (or some kind of computer-like message indicating that the Domina connection was severed.)
The player would have to click a button labeled "TERMINATE GAME." to acknowledge the ending. Then crash to desktop.
This would add a lot of narrative payoff to an otherwise mundane ending, since the player gave up an otherwise average game for a guaranteed Game Over and they *made Domina sad*.