Better faith based on what, exactly? And given that we were fighting an entire country which had openly and repeatedly declared they lived by an interpretation of Bushido that meant that they would all fight to the death, and had murdered millions of people to prove it, what is your criterion for determining the difference between implacable common sense, and implacable self-rightiousness?
Quite frankly, your position seems to be based on that same implacable self-rightiousness you are decrying, as if situational pursuit of peace is unarguably superior to fighting by default. In which case, just exactly how would you propose people muster the implacable violence necessary to destroy totalitarian monsters?
Or is that a debunked postmodern dichotomy which has been found to be the cause of inciting self-defense aggression in poor, misunderstood totalitarians, and so serves as it's own negation?
The debate is not between a united front of participants at the time (plus you) and later critics that you wanted to paint as philosophically unreasonable. It was a live issue at the time, and the correct position was seen and advocated, by clear sighted, rational men holding the gravest responsibility. It just wasn't acted on.
Next reading comprehension. Good faith in negotiations is a term of art that means making demands that are one's actual demands, making them openly and plainly, being as good as one's word, and expecting the same. It means agreement is the actual goal of the negotiations, not playing to a gallery or other extraneous goals. It is usually contrasted with negotiating in bad faith, marked by taking positions that are not one's own policy demands, purely for bargaining purposes; holding out things one doesn't want as bargaining chips, negotiation purely for show and consumption by third parties rather than seeking agreement with the counterparty, deliberate "crossing" behavior of asking not for what one wants, but what one expects the counterparty to be reluctant to give, and the like.
It was in bad faith to demand terms that implied removal of the emperor when there was no need or intention to remove the emperor. It was done for the sake of third party consumption (the electorate, the Russians), and for glory or the appearance of power or of consistency - to appear not to need to negotiate.
What I called "implacable self righteous" is exact and means somehting, it is not a free floating denuncifier. The desire to appear implacable means "cannot be placated", means "will not negotiate". Men may feel a subjective sense of power in it and third parties may even so perceive it, but it is not a source of power itself. It consumes it, spends it. Power gets what it wants and minimizes and neutralizes opposition effectively.
An accepted ultimatum would not have ended the war any less effectively. A rejected one that had been more reasonable and in better faith, would not have precluded the course of action actually taken to win the war.
What you call "situational pursuit of peace" is simply the moral and reasonable demand that the aims of war be kept constantly in view throughout its course, and the continuation of war be subordinated to achieving them. This is in contrast to war for its own sake, war as punishment, war to annihilate the adversary rather than achieve his compliance and one's own political aims. It is the subordination of war to political direction and rational control of that direction for civilized ends - in contrast to, say, a deliberate war of annihilation as Germany proclaimed in Russia, to pick an example.
The US wanted Japan to cease hostilities and to submit to occupation and demilitarization. If it could achieve those ends with less loss of life and no cost to their actual achievement, it had a clear duty to do so. If that depended on the Japanese as well (it did), then the US's duty in the matter was limited to offering that outcome in good faith. It would then by Japan's duty to accept it, on recognizing that keeping the emperor was the only political aim for which they were fighting that the allies would conceed in practice, and that their military situation was hopeless.
Ambassador Grew and Stimson saw this, and Stimson in particular also clearly saw the gravity of the ultimatum. He knew what the atomic bomb meant, not just for the end of that war. As for what knowledge of Japan was behind their proposal, Grew knew Japan better than anyone else involved in the US decision making process. He knew what the emperor meant to the warrior code of the Japanese military. He knew how futile it was to threaten them with a destruction they gloried in accepting, compared to appealing to a point of honor. Stimson heard him out, and gave his mature judgment - among the best ever to serve the United States or any great power, on every sort of subject, I might add - that a clause saying the emperor could remain if Japan laid down arms, would materially increase the chances of the ultimatum being accepted.
There is every reason to believe that judgment is correct. It would have materially increased the chances of the ultimatum being accepted - without raising them to certainty, admittedly. It cost nothing, and it had a significant chance of saving the lives of half a million human beings.
It was wanton to reject that advice. Stimson was right, and Truman was wrong about it.