The only ways for the Mormons to had a de facto independent state of Deseret is, as mentioned:
1) Buy the land from the Spanish/Mexicans first
2) US balkanization (possibly from CSA victory in Civil War)
3) Divine Intervention
Part of me wants to say "armed rebellion," but the Nauvoo Legion counted in 1857 at roughly 5,000 men. That's nothing compared to the US armed forces which would partake in the Civil War just a few years later.