Here's why:
a) You can't predict what would have been the result. That kind of moral calculus is impossible, and of course the troubled conscience is strongly motivated to continually inflate the estimates of what wouild have happened if #2 had been chosen.
A highly competent writer friend of mine, Mary Meehan --- much more competent in the investigative area than I am --- analyzed Truman's diaries and public statements on this subject. At first, he said the atomic bombing saved "n" lives. As time went on, and the body count from Hiroshima and Nagasaki went higher and higher, his estimates of how many lives it saved went to "2n," "3n," "25n" and so forth. A decent man doing what an appalled conscience needs to do, short of confession and repentance.
b) Saying that we can do any evil, even great evil in the eyes of humanity and God Himself, that greater good may come of it, is a line of moral reasoning that will be used to justify any sin. It's how Eve justified the first one.
Not to invoke the Argumentum ad Hitlerum, or even the Argumentum ad Saddam Husseinium, let's objectively note that it undercuts any possibility of arguing against any grave evil from infant craniotomy on up, if the doer thereof convinces himself that it was necessary to avoid a greater evil.
This boils down to "Thou shalt not commit murder --- unless thou art really, really tempted."
It makes you an enemy of God. Not a good bargain.
I understand your argument, but it is based on error.
You could not pick #2 rationally, because you would have already, as Truman did, had the combat experience of Saipan and Okinawa to base your estimates of military and civilian casualties.
To condemn another 250,000 of your own soldiers to death needlessly to argue a moral principle would have made you complicit in the murder of 250,000 innocent men.
The whole question of millions of Japanese dying also would just be icing on the cake.
In 1945, for a President to do any less would have been a grave moral error.