> The Japanese knew full well the limitations of the Soviet's naval and air capabilities, and they knew that the Soviet's had zero chance of mounting an invasion of their home islands was extremely limited.
It's not obvious to me that this was the case. In August 1945 most of the Japanese fleet was at the bottom of the sea, and they didn't have enough fuel for the rest. Ditto the air force -- there wasn't enough fuel, and pilots were poorly trained 9not enough fuel to train them).
The USSR in 1945 had thousands of effective fighter and bomber aircraft that could have won air superiority over the waterways needed to invade Japan. The distances an invasion would have to travel aren't enormous: 50 miles from Tsushima or 20 miles from Sakhalin. The Japanese would have found it difficult to send reinforcements against the Russian beachheads, because, again, they had little fuel, and Russian aircraft could have bombed the railways, putting them out of action.
Once the Russians had got a sizable body of men ashore, it would have been difficult or impossible for the Japanese to dislodge them: the Russian army was much better equipped and led than the Japanese army, and had just beaten the best army in the world. Japanese courage and self-sacrifice wouldn't have been able to make up that, any more than it was against the USMC.
The biggest difficulty I see for the Russians is whether they would have been able to cobble together enough ships to transport the necessary men and equipment.
Having said all that, Japan was deeply deeply fucked before Russia entered the war anyway.