How is it more complicated than (a) the Japanese were not willing to surrender before the atomic bombs were dropped (and not willing even after the first was dropped), and (b) the Americans didn't want any more of their troops killed than 'necessary'?

You don't have to take anything the Americans said into account, but to merely look at the actions of the Japanese themselves:

Two atomic bombs being dropped on them was not decisive in getting the Cabinet to decide to surrender. It took the Emperor's involvement to break the deadlock and even then there was a coup attempt to stop the surrender:

* https://en.wikipedia.org/wiki/Kyūjō_incident

And even those things were only barely over the line:

> When word of the emperor’s decision reached General Toroshiro Kawabe, the Vice Chief of Staff of the Imperial Army, he noted in his diary that he concurred with another senior general in doubting that the overseas commanders would comply with the emperor’s order. That these officers correctly doubted even an order from the emperor would secure compliance with key parts of the armed forces, was swiftly confirmed by messages from the commanders in China and the Southern Area, declaring they would not comply with the surrender. Their commands mustered between a quarter and a third of all Japanese servicemen. It took Hirohito’s personal emissaries to persuade these commands to surrender.

* https://www.nationalww2museum.org/war/articles/japans-surren...

Those two reasons are IMHO sufficient to me (as a non-American).

How else would you get the Japanese to surrender? AFAICT, this could have been done in the (i) 'traditional' way with troops invading the Home Islands, or (ii) with the atomic bomb. The estimates on the land invasion:

> The U.S. Sixth Army, which would invade and occupy Kyushu, estimated 124,935 U.S. battle casualties, including 25,000 dead, plus 269,000 non-battle casualties (disease, accident, etc.) for Kyushu alone. The JCS came up with an estimate that a 90-day campaign on Kyushu would cost 156-175,000 battle casualties, with 38,000 killed in action. By late July, the JCS was forecasting 500,000 casualties at the high end and 100,000 at the low end. In late July 1945, the War Department provided an estimate that the entire Downfall operations would cause between 1.7 to 4 million U.S. casualties, including 400-800,000 U.S. dead, and 5 to 10 million Japanese dead. (Given that the initial Downfall plan called for 1,792,700 troops to go ashore in Japan, this estimate is indeed most sobering, and suggests many more troops than planned would need to be fed into a meat grinder).

* https://www.history.navy.mil/about-us/leadership/director/di...

The US (Truman and others) concluded that they were not willing to have Allied troops suffer just the Japanese refused to accept the reality that they were beaten (which the Japanese knew themselves in 1944). And while the deaths of a few hundred thousand Japanese from the atomic bombs is regrettable, the lives of several more million Japanese were spared.

What other method(s) of ending the war with Japan do you use besides the above (i) or (ii) above?

Please, I'm curious to know, what scenarios you / "the rest of the world outside the US" think were possible. Can you outline them?