It's a question that could go back prior to their attack on PH. (Do we allow them any of their desired Greater East Asia Co-Prosperity Sphere, seeing their point about our grip over the Western Hemisphere with the Monroe Doctrine? I don't know.)
In other words, the guidance would have to have preceded our entry into the war; otherwise, you're handing me a schitt sandwich and laughing when I have no options.
The short answer is to fall back on the naval blockade. The US Pacific Fleet at war's end was the largest armada assembled in the history of the human race. We could have had warships doing donuts around those islands for years; there's no need for an invasion and we achieve our objective of a restrained Japan.
Put them in place and give the Japanese a phone number where we could be reached when they're tired.
You have yet to address the very serious objection I have already raised multiple times:
Your method would have been a slow method - and the ending of the war would have, as you admit, been according to the timetable of the Japanese.
Meanwhile, hundreds of thousands of Chinese were being killed by means of bacteriological warfare. Meanwhile, Allied POWs were languishing under inhumane conditions in Japanese camps. Meanwhile, Japanese children were starving to death. A naval blockade would have only prolonged those evils.
The A-Bomb may not have been, objectively, as lethal as fire-bombing - but the psychological impact of seeing an entire city destroyed by a single bomb was apparently what it took to make the Japanese military finally see reason.
I affirm once again: The dropping of the A-Bombs was the quickest way to terminate the war and put an end to immense human suffering (on both sides)! It was a terrible but simultaneously also the most-compassionate solution! The U.S. was entirely justified in using it!
It's a question that could go back prior to their attack on PH.
Why not take it even farther back, to Admiral Perry? You are attempting to muddy the waters / unnecessarily expand the scope of the question.
Regards,