Such a model of China is what I'm thinking of, I agree fully.Actually, I think a state that unified the Non-Denom definitely could unite the entire US. It wouldn't be cultural unity, every area would still be very distinctive. But a united Non-Denom world will advance faster than the New Israelites and can begin encroaching on their lands through aggression and assimilation starting in the early modern era, and then a state which governs both sides of the Mississippi will be very difficult to resist for the states further west. It's still possible for the western peoples to have recurrent periods of resistance that finally see them freed from the Non-Denom but it's worth noting that the Qing included many lands of non-Han people which evaded the Ming, lands which remain part of the Chinese state today.
1) I do think east of the Rockies will definitely be equivalent as "America Proper" to "China Proper" in terms of ethnocultural and ethnolinguistic stuff, and west of them your Xinjiangs, Tibets, Inner Mongolias, etc.
2) Dunno what equivalent the Pacific Northwest would be as I rambled in my other post in the other thread. It didn't have the dominating cultural quirk of the Mormon religion for Deseret despite that region being settled by Anglo-Americans, or the existing colonial Hispanic-reinforced-by-Mexican immigration/Chicano-formed-culture the OTL Southwest has, though - what with it being settled by regular American citizens, immediately integrated into the Union politically, and the easiest routes (relatively speaking, of course) to take through the Rockies in terms of physical travel versus the highest of the Rockies to deal with for Deseret and the Southwest. Those would be points to it being potentially integrated 'easier' or even potentially permanently so by/into this neo-USA. Maybe it's equivalent to Manchuria becoming utterly Han Chinese as a region fully "Americanized" through settler colonization and sheer cultural assimilation of the local natives alike? OTOH it does have a completely different religion, and established cities and states, versus the Great Plains and New Israelites' small nomadic numbers that could easily be swamped over with Non-Denom Neo-USA settlers.
EDIT: Extensive rambling added about the Pacific Northwest in this scenario.