And here's where I don't understand the reasoning: Did they seriously think the kokutai would have been preserved if they had fought on? Did they seriously think the Allies would have allowed Japan to continue as it had? It seems the most obvious thing in the world to blockade and bombard the Home Islands for six to eight months, destroying farmland especially, and then engage in the beachhead assault that had already been planned.
The American Armed Forces are still using Purple Hearts made specifically for the invasion of the Japanese Home Islands. They're all new-old stock, to use the common phrase; that's how serious the plan was.
Those planning Operation Downfall, the overall one to capture the home islands (well, the regime would fell after the 2nd invasion of the main island), who didn't know about the Manhattan Project were planning to make liberal use of chemical weapons. Those who did ... well, if the 2nd bomb failed, there's a very good chance future production would be reserved for Olympic, with up to 8 of them being used....
As for their strategy, they started the war with an assumption that we weren't tough enough to see it through. It's said that the truth didn't sink into the IJNavy until we lost 2 Rear Admirals (2 stars) in a single night action off of Guadalcanal, in a body of water that earned the name Ironbottom Sound, so many USN and IJN ships were sunk there.
So when it came to the home islands, they hoped they could make it expensive enough we'd give up before the regime fell. Even after we'd firebombed all their major urban centers minus Kyoto (politically critical for the Emperor) and the 4 a-bomb targets and alternates....
It's a very good thing for the world everything came together in that August and they surrendered. And if I had a time machine, I'd never ever try to change anything in history going up to that point, the horror of those a-bombs, even if each caused less loss of life than the first Tokyo firebombing (in only it and one other attack did everything come together including the weather and winds).
August 7:
1. Japanese nuclear scientists determine that the bomb was indeed nuclear device.
2. Imperial Navy estimates that US has only one or two more bombs and Japan could endure the attacks.
August 9:
1. bombing of Nagasaki
2. USSR declares war to Japan & Manchurian Strategic Offensive started.
3. Hirohito worried because USSR declared war and held an Imperial conference that authorized minister Tōgō to surrender with only one condition: status of the Emperor must be preserved.
August 15: Japan Surrenders
Even after Hirohito made the personal decision to surrender, the intention was to continue the war if the kokutai (Imperial institution and national polity) would not be preserved.