Yeah, I've been reading about WWII for 50 years and this the first that I've heard that the Japanese "were close". Maybe they were, doubtful it would have changed things because......
By late July, 1945, we had been systematically firebombing the main Japanese cities killing hundreds of thousands of their people. They had broken up industry into a many house-based "you do this step" in war production so the decision was made to take out cities, more or less. That campaign, using B-29s in low altitude bombing runs dropping magnesium bomb-lets, started with the "Meeting House" raid on Tokyo March 9 (100,000 dead in that raid). In the almost 5 months before August 6, the Japanese had come up with no way to counter these attacks.
Also by late July 1945, the U.S. submarine fleet had effectively cut off Japan from receiving any large scale supplies, especially food. Japan basically couldn't feed itself so probably slow starvation was on its way. The Japanese had no capability at that point to stop the American submarines.
By the end of July, Emperor Hirohito wanted a way out to end the war to stop the killing but politically he was unable to stop the war party (Tojo had been replaced as prime minister already). The 2 American atomic bombings on August 6 and August 9 (Nagasaki that day was actually the secondary target, I forget the primary target but the A-bomb B-29 crews were under strict orders that the bombing aim point had to be clearly seen and it wasn't, so bad news for Nagasaki). This new development gave Hirohito an "out".
Between August 9 and August 14/15, Hirohito put out peace feelers to the Americans so basically the last two weeks of August was sort of truce situation before the official surrender happened on Sept 2 in Tokyo Bay on board the USS Missouri
(remember Truman was from Missouri). Even during that mid-August time period, various war party officials were attackers/killing multiple people Hirohito had trying to work out the surrender deal. A smaller military coup against him failed. Hirohito was generally a weak leader during the time period 1931 through 1945 but he grew enough of a pair to make his military stop the war by the end of August. He knew they were beat, why keep the killing happening...
A dated but good book on that month is The Fall of Japan
(1967) by William Craig. Google the title and his last name, and lots of used copies are available so its still widely read today. I read it the first time in the late 1970s... https://www.goodreads.com/book/show/26834513-the-fall-of-japan