Was wandering around and found the Great Khans, triggering their Legion alliance quest before getting it from the NCR. Didn't advance the quest any further than picking it up; ie, talking to everyone in the Longhouse, getting told by the guy outside to speak with the lieutenants and (optional) deal with Karl.

Left, did some other stuff, advanced NCR quests and then got For the Republic, part 2: go and deal with the Great Khans.

So returned to them, finished up the plot, presented the evidence about Karl, and convinced the Khan's to break their alliance. Went with the 75 speech check about them having no legacy.

Oh My Papa quest completes. For the Republic, part2, does not update. Spoke to papa khan and Regis and neither of them have any further options. Returned to Moore, and there is no option to update her about the quest -it assumed I am still doing it, and the quest log tells me to 'deal or destroy' with the khans still.

However, my Wild Card quest says I can return to Yes Man to tell him the Khans will sacrifice themselves. But this won't advance For the Republic, leaving me stuck.

I don't have a save that won't involve losing about 8 hours worth of gameplay, which I am not willing to do. Are there any options to resolve this, including use of console commands to trigger this section of For the Republic complete and advance it to the next one with the Ormetas?

According to Wiki the quest has a high rate of getting FUBAR at this point. I assume the only thing that could save you now is console commands.

Well, I tried kiling all the Khans and that worked to move the quest on. SO I just have to accept that my character is a mass murderer, from time to time.

Moore's dialogue options do not check whether or not Oh, My Papa was already underway when you get to that portion of For the Republic, Pt II, and as a result it does not get marked as 'completed' in her checklist since as far as her script is concerned you haven't actually started it yet. For this reason (and a couple of others as well), it is highly advisable to delay starting Oh, My Papa until prompted to do so by one of the main quest lines.

As the quest is already completed, about the only options are to either reset it via the command console or reload a save prior to starting it in the first place. Note that the command route may also require further commands to prod Moore's 'memory' so that she acknowledges your completion of the quest.