Let me first retract my statement. Given the sources you cited, I concur the Soviets did have plans to invade the northern island. My original reaction was based on the premise you had confused the Soviet invasion of Manchuria with an invasion of Japanese islands.
I also knew others have previously argued that dropping A-bombs was unnecessary to defeat Japan and that the bombing was done primarily to keep the Soviets out of Japan. So let me take back any assertion that you made that up.
Instead I will argue the main point: that the a-bombs were dropped primarily to bring a quick end to the war and secondarily to curb potential Soviet influence in post-war Japan.
A key point is that the US had been pleading since 1941 for the USSR to enter the war against Japan. Stalin however had enforced such a strict neutrality that American aircraft attacking Japan were forbidden the right to use airfields in Siberia. I think the record is clear: that Roosevelt at Yalta in February 1945 finally got Stalin to agree to enter the war against Japan. Even at that late date, knowing that a-bombs were nearing completion, Roosevelt and his military advisers felt the US needed help defeating Japan. The record is also clear that Roosevelt agreed to give the Soviets territorial concessions in Manchuria and Korea in return for Stalin opening a front against Japan. I have seen nothing that says the US had made any concessions regarding Soviet occupation of Japanese home islands. There was agreement to Soviet occupation of a few Japanese controlled islands in the north near Siberia, but that did not include Hokkaido.
The record is also clear that the Americans were planning an invasion and the Japanese were preparing to try and stop them.
As contemporary sources indicate, American military planners feared over half a million or more American casualties. This was their realistic assessment based on their actual experience with amphibious invasions against the Japanese. Further, the advent of Japan’s large scale use of kamikaze tactics was leading military planners to revise their casualty estimates upward.
The record is also clear that the plan was to drop two bombs in quick succession just after the Soviets started to invade Manchuria was designed to achieve a psychological impact that would result in a quick surrender. It was felt that other ideas like merely demonstrating the power of the a-bomb would not be impressive enough to get the Japanese to give up. These alternatives all promised different variations of long wars of attrition with large numbers of people killed on both sides including huge numbers of Japanese civilians. The Americans believed they understood enough of the Japanese culture at the time to know the Japanese would have a hard time surrendering even knowing their cause was lost. People years later try to retroactively implant their sensibilities into the minds of wartime Japanese and say they would have surrendered, but that is not the way they were thinking at the time. People also years later look at Japanese diplomatic overtures with a gullibility not shared by Allied leaders at the time. Compromises that left Japan unoccupied or kept the Emperor in place were what the Japanese wanted, but those were things Allies would never accept.
The telling proof is that the Japanese war cabinet was tied on a vote to surrender even after the Soviet invasion of Manchuria and after a-bombs were dropped on two Japanese cities. It still wasn’t enough. It took the Emperor to cast the deciding vote. Even after that, there was a coup by junior officers to overturn the surrender and it almost succeeded.
The Soviet invasion of Manchuria that the US had been asking for certainly did help. However it is a distortion of the historical record to say the main motive in the US dropping the a-bombs was to prevent Soviet occupation of Japanese home islands. First and foremost, it was done to get Japan to surrender quickly and thereby save American lives.