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Remnant in the Time War? I could see themselves as allies with the Time Lords, since the Daleks main goal is extermination. As for how they would do, I think Huntsmen and Huntresses would provide good reinforcements for ground level. But if the Daleks use spaceships and bombard the planet from space, Remnant's screwed. As for recruitment, I could see Rassilon try to recruit Salem. He could offer her a chance to go back in time and either prevent her curse or save her children.
Ozpin and Ironwood may fear both factions, but will have Remnant's fate to consider. They might go with the Time Lords. As for the 8th Doctor or War Doctor, I could see him trying to destroy Remnant. I mean, he almost destroyed Gallifrey.