Let x = outcome. Let y = action in question. Let z = other action(s).

x > y + z.

Let's use your example of WW2.

Winning the war = x. It was good. Let's say an arbitrary value of 100.

Collateral damage = y. Let's give it a value of -90. It's universally "bad."

Other, less questionable war efforts = z. Let's give it a value of -5. It's not "good," but can be reasonably accepted by most.

To solve our problem:

100 > -90 + -5 (or -95)

After the war, we were better than if we'd lost. But, it still was pretty awful all around.

The thing about it, to me at least, is that the action is still negative. To wrap it in the context of your class's thought experiment- it's still a moral wrong. "The greater good" does not negate that the action in and of itself is terrible. That should never be forgotten and I would forward that it's dangerous to even remove the label.

Consider the example of the mass murders of concentration camps. In any other context, those guards and soldiers probably would have not been complicit in such an abhorrent exercise. But, what the Nazi's did was to frame it in a larger context, as well as cultivating a mindset that those in the camp were "other." They soldiers and German people were indoctrinated to think that those exterminated "weren't German," or maybe even less human.

This made it so the guards didn't look at the morality of each action. Instead, they focused on the bigger picture, which they had been brainwashed to believe was paramount.

This, in my opinion, is dangerous. Should such a terrible choice have to be made then it should be with the full knowledge that a universal moral wrong is occurring. There's no reason to strip the action of it's "negativity," unless you want to create an army that doesn't think. Should the greater good really be greater then history will judge that accordingly.