If I were to try and construct such a scenario, I'd do my best to move the Mormons to Salt Lake a bit earlier. Either due to their friction with Mexico or simple American leanings, they, like California, declare independence as a Republic. Being a bit in the hinterlands, they can't immediately cede authority to the US. They're also able to very quickly form a provisional government, since it's basically just the Mormon power structure. The US, not knowing as we do that it was going to be a knockout, quickly seizes the advantage and recognizes the Republic. Now, is it likely that the US would negotiate Deseret's independence as part of the treaty with Mexico, before it's locked down that Deseret would become a state? I don't know, I'm asking - folks? If you'll permit me the assumption, we come out of the war with a US recognized Deseret. But what now? Suddenly some people aren't so sure they want to annex a new state full of polygamist heretics who sound at times suspiciously abolitionist? For state they must be, under the precedent established by Texas - or so they say. And unlike in OTL, they are not under US law and power, and bargain from something of a position of strength. The Mormons are resistant to giving up their traditions. The US is resistant to allowing them to retain them. Negotiations collapse, and part of the Compromise of 1850 is to drop any further attempts for the time being. California is the new free state - maybe Deseret can be admitted in the future, a balance to a slave state carved from the new Mexican territory. But that perfect chance never quite comes by the time of the Civil War, and then the Union has bigger problems...
EDIT: Hmm, but why move early? Proposal: From (what I assume would be) the intolerance and instability of Augustan (or post-Augustan) Britain, young Emma Floyd (later, in OTL, Emma Hardinge Britten) emigrates to America early. She falls in with the Mormons, and with her visions of the future and powers of clairvoyance, encourages the early and vague ideas of a Salt Lake migration.