This was not possible, the Allies had all agreed on unconditional surrender so no separate peace could be carved out.

Yes—and beyond the important question of separate peace, those conditions were seen as too onerous given the perceived need to transform Japan's political and social institutions after the war. Beyond this was the political requirement to address widespread and well-known atrocities committed by the Japanese Army, as well as the failure of voluntary arms control treaties in the interwar period.

In the end, of course, the Allies did decide to leave the Emperor in place as nominal head of state—but had not decided to do so before the Japanese capitulated, and certainly did not want to commit themselves to that course.

Exactly. And the Allies included the Soviets, who were thus rather cold to aiding a negotiated surrender.