I'm not going to read four pages of this, so if i'm repeating anything somebody let me know.
Whether they were justified or not is complicated. As far as overall casualties as a direct result, neither bomb was as effective or cost efficient as a convential firebombing would have been. However for general shock value they were certainly unparalleled. And in their goal of convincing the Japanese to surrender they were an unmitigated success. It is possible that just carpet bombing or firebombing the two cities would have been enough to convince the Japanese to surrender, but this is unlikely as no previous conventional bombing had that effect. So far, then, they were justified.
If we take into account though the long term effects of the radiation, and the psychological effects of the total annihalation of two cities, the bombs do seem to be over powered and extravagant. The total obliteration of two cities and their populaces would still have more or less happened by fire bombing, so that is really just semantics. As for the radiation, it seems clear that the American government and military would not have known or considered the full effects of irradiating a population center and the surrounding farmland, despite what studies were done. but ignorance is no excuse, as the information would have been available to them regardless. Taking this information into account, were the bombs were jusitified? Maybe.
Taking a closer look at the goal of forcing Japanese surrender, some things need to be examined. the cost of human life in an invasion of the mainland would have numbered in the many millions, and primarily been japanese people, with as much as a 1:10 ratio of Allied to Japanese casualties estimated by American Military sources. Surely the bombings were prefferable to that. Yet after the first bomb was dropped the Japanese made overtures that indicate they were going to surrender. They were however not absolute in the manner of conveyance, and instead of waiting for what would have surely been a decision to surrender, the American military dropped the second bomb. Thus the second bomb was certainly unjustified under these paramiters, but the first was.