You've quoted or mentioned all the relevant conversations in which the Oracle explains why she helped Neo: she wanted the war to end, and for the humans and machines to finally "get there together" (to the future) in peace.
However, the Oracle was not the only machine that wanted peace -- even the Architect was unsatisfied with the Matrix and The One system:
[The Oracle] stumbled upon a solution whereby nearly 99% of all test subjects accepted the program, as long as they were given a choice, even if they were only aware of the choice at a near unconscious level. While this answer functioned, it was obviously fundamentally flawed, thus creating the otherwise contradictory systemic anomaly, that if left unchecked might threaten the system itself. Ergo those that refused the program, while a minority, if unchecked, would constitute an escalating probability of disaster.
The Architect, The Matrix Reloaded (source)
Not only was the system flawed, but there were real dangers to the machines -- the Matrix was inherently unstable, and if the One couldn't be blackmailed into rebooting the Matrix the machines would be forced to endure "levels of survival [they were] prepared to accept"1 (the extinction of humanity and lack of that power source for the machines).
The difference between the Architect and the Oracle isn't that the latter wanted peace while the former wanted to maintain the antagonistic system of the Matrix and The One -- it's that the Architect just did not know how to create peace between the machines and humans. He tried to create a peace with his first Matrix -- a symbiotic Paradise Matrix "where none suffered, where everyone would be happy"2 while the machines would be able to safely extract power from humans (certainly a vast improvement over the Machine War that occurred in the real world and resulted in the destruction of the sky). Of all the ways in which the machines could have dealt with the humans defeated in the Machine War (e.g., kill them all, put them in a real prison with no simulation, simulate an explicit reward/punishment system for cooperating/resisting, etc.), the machines chose perhaps the most peaceful option they could get to work. While that doesn't prove the Architect was trying to develop a peaceful solution, it does show that peace was a secondary objective (behind the primary objective of the machines' survival) even if the objective of peace was entirely self-serving on the part of the machines (peaceful coexistence with humans is less dangerous than humans constantly trying to resist their imprisonment).
Unfortunately, the Paradise Matrix failed so such a peace was not an option. It failed because
You and I may not be able to see beyond our own choices, but [the Architect] can’t see past any choices.
The Oracle, The Matrix Revolutions (source)
The Matrix and The One system was therefore developed by the Architect and Oracle working together as a replacement for the failed Paradise Matrix. This system introduced some level of human choice (though only at a "near unconscious level") which met the primary objective of ensuring the machines' survival (by using the humans as a power source) and the secondary objective of peace in a limited fashion (by keeping most humans from resisting), though of course it too was flawed since not all humans accepted it. Still, it "functioned" even though everyone from the Architect to the Oracle knew it was flawed.
This system worked for several iterations until Neo's. Neo's iteration exhibited several differences from previous ones: Neo loved Trinity instead of all humanity generically, and Agent Smith had become a virus that could destroy not only the Matrix but also the Machine City. These differences allowed the Oracle to seek a more stable solution: she knew Neo could be encouraged to not return to the Source like The One is supposed to (and that he would actually make that choice because he wanted to save Trinity), and that the consequent failure of the Matrix and the virus Smith would provide Neo with the leverage he needed to strike a deal with the machines to work together to destroy Smith and end the war -- thus ensuring the survival of both the humans and machines, and finally achieving peace.
The Architect did not approve of the Oracle's actions during Neo's iteration because they were risky:
The Architect: You’ve played a very dangerous game.
The Oracle: Change always is.
The Architect: Just how long do you think this peace is going to last?
The Oracle: As long as it can.
The Oracle: What about the others?
The Architect: What others?
The Oracle: The ones that want out.
The Architect: Obviously, they will be freed.
The Oracle: I have your word?
The Architect: What do you think I am? Human?
The Matrix Revolutions (source)
However, the Architect's disapproval of the Oracle's actions doesn't mean he didn't desire a better, more peaceful solution, too. It is simply that, compared to the Oracle, the Architect was more willing to maintain the system of the Matrix and The One only because he couldn't come up with a better solution and didn't understand how to account for human choices. Only the Oracle knew how to account for human choices and predict the future, so she was able to attempt to find a better, more stable (i.e. peaceful) solution on her own.
One can liken the situation to the machines operating with a calculus of maximizing their chance of survival, and the Matrix and The One system was like a local maximum which ensured their survival (but not a truly peaceful coexistence with humanity), whereas the machines' survival and peaceful coexistence with humans was a global maximum that they had not achieved. The path from the local maximum the machines had achieved to the global maximum involved serious risk -- humans started the war in the first place so the machines were understandably reluctant to just stand down and hope the humans would stop resisting (and continue providing power). The Architect -- and probably most, if not all, of the other machines -- could not see a path to reach the global maximum because he/they could not understand how to account for human choices to get there. Only the Oracle could do that.
1The Architect, The Matrix Reloaded
2Agent Smith, The Matrix (source)