The problem was surrender was never (until the bombs) going to include unconditional surrender, which the US required. Directly from the Potsdam Declaration:
the elimination "for all time [of] the authority and influence of those who have deceived and misled the people of Japan into embarking on world conquest"
"Japanese sovereignty shall be limited to the islands of Honshū, Hokkaidō, Kyūshū, Shikoku and such minor islands as we determine." As had been announced in the Cairo Declaration in 1943, Japan was to be reduced to her pre-1894 territory and stripped of her pre-war empire including Korea and Taiwan, as well as all her recent conquests.
"The Japanese military forces shall be completely disarmed"
"We do not intend that the Japanese shall be enslaved as a race or destroyed as a nation, ... The Japanese Government shall remove all obstacles to the revival and strengthening of democratic tendencies among the Japanese people. Freedom of speech, of religion, and of thought, as well as respect for the fundamental human rights shall be established."
"Japan shall be permitted to maintain such industries as will sustain her economy and permit the exaction of just reparations in kind, ... Japanese participation in world trade relations shall be permitted."
This was offered 10 days before the bomb, yet the Japanese rejected it outright. Why would they do that if they were 'seeking surrender'?
Additionally we have their diplomatic cables from the time because we had cracked their codes. So we have insight into what they were trying to do before the bomb. "magic" diplomatic summary.
June 22nd: The Emperor gathers his "big six" advisers to discus peace plans. "I desire that concrete plans to end the war, unhampered by existing policy, be speedily studied and that efforts made to implement them." It is decided the best way for that to happen is to solicit the Soviets as they appeared to be their best bet to solicit peace with the Ally forces (they had attempted to plan peace before, but the Yalta Conference all but ended relations between the Allies and Japan).
June 30th: FM Togo tells Ambassador Sato to establish to try to establish a "firm and lasting relations of friendship" with the Soviets. The Soviets responded by delaying their talks and not promising Japan anything. There is debate on why exactly the Soviets stalled, but more on that later.
July 11th: Sato is finally able to hold a meeting with Soviet Foreign Minister Vyacheslav Molotov. This meeting, as their talks had gone, went nowhere. As a result, Togo instructs Sato to tell the Soviets "His Majesty the Emperor, mindful of the fact that the present war daily brings greater evil and sacrifice upon the peoples of all the belligerent powers, desires from his heart that it may be quickly terminated. But so long as England and the United States insist upon unconditional surrender, the Japanese Empire has no alternative but to fight on with all its strength for the honor and existence of the Motherland". (I bolded what I believe to be the most important part of this).
So already on July 11th we knew that unconditional surrender was never going to be accepted. This is backed up by internal communications where Togo states:
With regard to unconditional surrender we are unable to consent to it under any circumstances whatever. ... It is in order to avoid such a state of affairs that we are seeking a peace, ... through the good offices of Russia. ... it would also be disadvantageous and impossible, from the standpoint of foreign and domestic considerations, to make an immediate declaration of specific terms
They were not going to accept any peace that called for unconditional surrender from Japan. Their Emperor was not going to allow it, and didn't until we dropped two atomic weapons and firebombed their capital. While horrific, and something that we as a country can regret, it was unfortunately necessary.
Finally, as an aside, it is advised that you not cite the Institute for Historical Review or take anything it states as fact. It is a known historical revisionist center, specifically in regards to Holocaust Denial. Bring that to almost any historian and you will be laughed out of the building.