So House or Independent ? Would Graham be wiling to help the NCR? What do you think Graham would do in my shoes?
I'd go with statements given by the Dead Horses. If you use Sneering Imperialist on the one who greets you in the cave, she basically says she'd like to kick your ass, but won't because Graham said not to fight with someone unless they start the fight first. In that sense, I suppose he could fight alongside the NCR too, since he also mentions "they can be saved." Simply refuse to kill the Khans, do the peaceful ending with the Kings and with the BoS, I honestly don't know if Graham would bother since the group is so hateful and aggressive towards outsiders.
Kinda tough to say since none of them are believers.