Before I read your actual posting, the conclusion of DOOMSDAY MACHINE automatically shot to my head. But I'm going to have to think long and hard on this one. For now, if we include the first six movies, I have to consider the destruction of the ENTERPRISE in THE SEARCH FOR SPOCK. It's the ultimate undoable moment in Classic Trek, whether they get a replacement lookalike ship or not.
Leaving out the films, the next moment that comes to mind is the death of Alexis Carringt------I'm sorry, Edith Keeler.