Maybe, but there's no guarantee that an allied invasion of Japan would have been necessary in the first place. This fanatical belief in self sacrifice has been overplayed, in my opinion. The Japanese war morale was certainly declining, which is why the nuclear bombs worked in the first place. Dozens of Japanese cities had already been essentially destroyed by conventional terror bombing. The Japanese were holding out hope that the Soviet Union would be a third party "peace talk" host, and those hopes were dashed when the Soviets invaded Manchuria instead.
I would also say that it is folly to look at the costly invasions of small, highly fortified islands defended by (in many cases) fanatical and experienced troops, and extrapolate from that the perceived costs of invading mainland Japan. Japan itself was far from as fortified, since the very purpose of this outer ring of fortified islands was to provide an area of control to indirectly protect the main islands. The invasion at Normandie has been called the largest invasion in history, but it's also a matter of history that in the first day of fighting saw only a few thousand killed, which compared to the huge land battles of the Eastern Front was nothing at all.
The Japanese didn't have some magical source of power of resistance that the Germans lacked. The allies had complete air and naval control, would soon have complete control of China from which to stage an invasion, and it was in the Emperor's best interest to avoid a long, costly subjugation of Japan which would likely have seen him tried as the war criminal he was. He had a lot more influence and control on the war effort than many people give him credit for, and he had a very real sense of self-preservation.
I am unaware of any historian who has ever called Overlord the largest invasion in history. If you mean largest naval invasion, then yes, it is that. However as an actual invasion, D-Day is small. D-Day being the designation for the designated day of the invasion so very small numbers of troops involved.
On day-0 about 150 thousand allied troops engaged I think 3 German divisions. That is less than 60k men. In terms of scale, that is small potatoes. It probably isn't even in the top 20 operations in the entire war.
By comparison. Bagration had millions of men involved. Barbarossa had almost 10 million men involved. There is a reason the casualties were pretty minimal in Normandy. While no doubt the fighting that did take place on Sword, Juno and Omaha was terrifying. There just were not that many men involved on either side in the actual fighting.
You are also completely wrong about the Japanese and their willingness to sacrifice. Their culture was completely different to our own. There are very real reasons why on many of the Islands the US cleared during the Island hopping campaign there were few if any Japanese POW's. In Europe the ratio of KIA to Prisoners is usually around 50/50. Once a unit takes 50% casualties and is overrun they tend to surrender. On the Pacific Islands this was not the case. Iwo Jima, garrison of ~20k resulted in 200 POW's. They didn't all die in combat either. Large numbers committed suicide. This is where the infamous Banzai charge comes from. The Japanese didn't just fix bayonets and charge as part of their typical tactics. These were suicide, desperation attacks. Germans didn't do this. Americans didn't do this. Russians (usually) didn't do this. Canadians didn't do it either. Desperation attacks like what the Japanese used in a systematic fashion were completely alien to every Western forces military.
On Saipan, Hirohito released a broadcast which basically told the civilians there that they faced terrible horrors at the hands of the Americans and encouraged them to commit suicide. They did in very large numbers, infamously flinging themselves off of cliffs.
Here is the reality of what was going on in Japan. The Diet was split between a dove faction and a hawk faction. The hawkish faction controlled the Emperor and controlled the diet. The doves were sending out tentative feelers to the Americans regarding a negotiated conditional surrender. The Allies had already agreed at Yalta and Potsdam that only unconditional surrender would be accepted. The dove faction had no real authority to send these feelers out in the first place, nor did they have the traction within the diet to do anything anyways. This is where the myth that Japan was about to surrender comes from.
Would the Soviet entrance into the war have shifted the balance far enough for the dove faction to take control of the diet? I personally doubt it, but it is possible. Truman had the choice of letting the war drag on, at the cost of tens of, even hundreds of thousands of dead civilians per week, or he could drop the bombs. To me the realpolitiking doesn't matter. It doesn't matter if they were trying to show the USSR they had the bomb. It doesn't matter if they were doing it to test them. All that matters are the hard numbers. More people lived overall, on both sides by bringing the war to a sudden end than to allow it to linger on potentially ending with an invasion.
The number of people who died between Hiroshima and Nagasaki is generally not really understood. Between both bombs about 100k people died. The after effects were not and are not as devastating as people think. Statistically there was a very minimal rise in birth defects in Hiroshima and Nagasaki, barely outside the statistical norm for the rest of Japan. The issue there is perception. EVERY Birth defect was blamed on the bombs.
In the end, my argument doesn't really care about the ferocity of the fighting that would have occurred in an invasion of the home islands. It would have been ferocious no doubt about it and brutal with extraordinarily high casualties on both sides. The US forces would have taken casualties at a sustained they would not have encountered since the civil war. My primary argument and concern is with the civilian population. The death toll in the civilian population would have been absolutely horrifying.
In the end, Truman made the only choice he could. Drop the bombs and make them surrender. I can't even imagine the outrage that would exist if Truman didn't drop them, the US invaded and a couple million Japanese and American soldiers died and on top of that 10 or 15 million Japanese civilians died.
On top of all this, most Japanese consider the bombs a tragedy but a necessary one to prevent a greater loss of life from occurring.