This matches the collection of ULTRA-decoded Japanese diplomatic traffic and notes from those close to the Japanese Supreme Council that I can't find online at the moment. [Notes mine.]

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

"[August 9] The news of the Soviet offensive sent the Supreme Council into urgent session, with Prime Minster Suzuki and Minster of Foreign Affairs Togo coming out in favor of opening a negotiating channel to the United States via Switzerland and Sweden, along with Navy Minister Yonai. Togo’s proposal to accept the Potsdam Declaration with the condition that the emperor’s position be preserved (something the declaration did not specifically address). The hardliners countered with a proposal that added additional conditions (which the Allies would certainly reject). [IIRC, these conditions were 1. No occupation of Japan, 2. The Japanese would handle the demobilization of their armies, and 3. The Japanese would perform their own war crimes investigations and trials.] As the discussion was going on, General Amani and General Umezu were secretly taking steps to implement martial law to prevent any such negotiations from happening at all. [I do not believe this was the same conspiracy as the attempted military coup several days later to prevent the emperor from broadcasting his surrender speech.] At 1030, Suzuki reported to the council that the emperor was in favor of ending the war quickly. Nevertheless, the council was still deadlocked 3–3 at 1100 when word of the Nagasaki bomb was received, and remained so even afterward.

"With the Supreme Council still deadlocked, the full cabinet met at 1430 on 9 August, again arriving at a 3–3 vote. Arguments raged in a series of meetings late into the night. Finally, Suzuki requested an impromptu imperial conference with the Supreme Council and the emperor, which commenced at midnight and continued until 0200. Finally, Suzuki informed the emperor that consensus was impossible and requested that Hirohito break the stalemate. The emperor sided with Togo’s proposal to make an offer to accept the Potsdam Declaration with the condition that the emperor’s position be preserved. Suzuki then implored the Supreme Council to accept the emperor’s will.

"On 10 August, the Japanese government sent a telegram via the Swiss, which was immediately intercepted by U.S. intelligence. As U.S. leaders evaluated the Japanese proposal, President Truman ordered a halt to the bombing of Japan and that the next use of an atomic bomb would require explicit presidential authorization (the second one didn’t). ...

"On 12 August, the United States responded to the Japanese offer, stating that “The ultimate form of government of Japan, in accordance with the Potsdam Declaration, to be established by the freely expressed will of the Japanese people.” The Japanese found the response to be ambiguous, which it was, provoking more heated discussion in the Supreme Council whether to hold out for an “explicit guarantee” of the emperor’s position. ...

"On 13 August, U.S. B-29s dropped leaflets all over Japan, making public the Japanese proposal and the U.S. counterproposal. A strong case can be made that it was actually the psychological impact of this huge leaflet drop that tipped the balance (making it one of the most effective psyops campaigns in history), although by this time the full magnitude of the collapse of Japanese defenses in Manchuria and Sakhalin Islands was also known to the Supreme Council, which finally agreed that the language in the U.S. counterproposal was good enough. [There were more bombings of Japan at this time, as the Japanese surrender message to the Allies was sent encoded and there was an increase in military radio traffic.]

"At 2300 on 14 August (Tokyo time) the emperor made a gramophone recording reading his statement to the Japanese people of his decision to surrender (without ever actually using that word), which was to be broadcast to the Japanese people over the radio at noon on 15 August."

The Japanese government at the time gave most of the power to the military (2/3 to 1/3 in the Supreme Council (and more given the pre-war tradition of assassination)) and that council was deadlocked up until Prime Minister Suzuki requested the Emperor to break the deadlock---the only time he cast a vote in the council, as far as I know.

Ground invasion (either by the US or more likely by both the US and USSR, leading to a split North and South Japan akin to Eastern and Western Europe) vs. atomic bombings is indeed a false dichotomy; the third option (favored by the US Navy) was to simply continue the blockade of Japan, leading to mass starvation. Oh, and this whole situation is made more touchy by the fact that the Japanese Army had 1,500,000 (?) men in armies on the Asian mainland. One concern was that if the Japanese government did collapse, there would be no one in a position to tell the military in Japan and in Asia to stop fighting.

Here's the deal about the USSBS: it's massive. The US let a big stack of social scientists and operations researchers loose and took everything they produced as part of it. And then wrote conclusions that accept parts of it and contradict others. If you want a conclusion, you can find it in there somewhere.

I do not know of any serious historians who accept the idea that Japan would have surrendered before the end of 1945 without any outside push. Certainly, they didn't seem to be in any particular rush even with the pushes.

Oh, and about just not using the atomic bombs? Truman addressed this later: what are you going to tell the parents of the soldiers who are killed after Aug 10? This particular war has been going on since 1937 (if not 1931); tens of millions of people have been killed. And you chose not to use a weapon that could have ended it?