Thanks to the citadel DLC it turn's out that they knew sovereign was really a reaper and that they decided to bury their heads in the sand with regards to their existence. Even if Cerberus's action against the reaper's weren't for the sake of protecting colonies at least they acknowledge their existence.
"They'll regret that soon the time for unity is now." Not to mention it was humanity who actively trying to build the only thing in the whole galaxy that is capable of stopping the reaper's from the get go.
What the turian's were doing wasn't going to be enough to stop the reaper's, the crucible that the Alliance was building is the only thing that can stop the reaper's and the game goes to great lengths to explain this to the player and the alliance alone can't build it.
Had other species had join in on the crucible earlier Udina might not have attempted the coup. The coup was a wake up call that the war is coming to them one way or the other and that the time for inaction had long pasts since the reaper's arrived. Also the crucible was ultimately an Alliance project since it was overseen by Admiral Hackett so its not far fetched to say human's were indeed spare heading the war against the reaper's.
Fighting Cerberus didn't stop the alliance from building the crucible from the get-go. I'm sure the other species could've spared one or two small team's to lend a hand with the crucible from the get-go as well.
Yes, they knew Sovereign was a Reaper but STILL blamed the war on the geth REGARDLESS of whether or not you have an ALL HUMAN Council in ME2. That is, the ALL HUMAN council is no better than the mixed one at responding to the Reaper threat. Humans are, therefore, not represented as being more noble than the other species at that point in the game.
The "they'll regret" line is nothing more than a common, threatening platitude uttered by people who want to bend another party to their will. It does not recognize the needs of the other party being threatened and does not indicate "nobility" (i.e. concern for the overall galaxy in this case). The primary motivation for the humans doing anything is still represented as being "saving earth" rather than "saving the galaxy." Saving the galaxy is represented as being viewed by the humans in the story as a "collateral benefit" of saving earth. If the humans could have saved earth while sweeping the rest of the species under the bus... they would have clearly done it.
The fact presented is that the "Alliance alone" cannot finish building the crucible nor can they even discern what the catalyst might be on their own (that ultimately takes cooperation from the Asari). You actually contradict your own statement in your last paragraph as well by criticizing the other races for not sending in small teams sooner. Also, you can start to gain some alien assets towards building the crucible very early in the game... so, the appearance of aliens sending in a "few small teams" can actually happen early in the game... depending on what priorities the player puts on various missions. For example, in first visit to the Citadel Embassies even before meeting with the council, one can overhear a volus actually say "Nevertheless, we are committed to helping both the Turian Empire and the Human Alliance."
Finally, lets talk about Udina - The suspicious placed on him by the Salarians are based, according to Bailey, on Udina accumulating large sums of capital... which is something Udina says he intended to do to help fund the crucible in one of the very first conversations in ME3 that Shepard can have with him RIGHT AFTER the very first meeting with the Council... so, Udina is, at the very least, rather quick to stop trying to convince the council to help and resort to Cerberus to raise funds for the Crucible, isn't he?... so, it's doubtful that his motivation is such noble desperation as you describe.
My point is that the "humanity as the great savior of the galaxy" is not as strongly presented nor is it as one-sided as was stated. The opposing view is also present and that is what the basis for a dichomotous RPG is - the ability to interpret what's being presented from both sides of the coin. Was it done to perfectness in the ME Trilogy... no, I would agree that there is still some imbalance. Was it done "horribly" - no, it was done rather well, IMO.