Er, maybe you want to gloss over, not emphasize, the fact that you didn't get around to answering the question of whether invading Europe (which obviously entailed much evil in the form of death and destruction) was justified in order to achieve good (the destruction of the Nazi regime).
The justification for the war isn't an example of the ends justifying the means for the State, but an example of the lesser of two evils --do nothing while innocent people are killed or war against the perpetrators. Warring against the Nazis was the lesser evil.