I think any of you others replying to the OP are definitely better qualified to respond to it; this is just not a part of history that I feel I know at all well.
Perhaps my chief motivation in chiming in was the hope of seeing this ATL Joseph Smith being treated as something more than a subroutine of alt-history implementationalism: if X is a concept, agent Y could make it happen!!! Liek f4evvar!!!
All I sought to suggest is that, given more time (and perhaps even peace) to think about his world, Smith might respond to it -- as someone who was not part of the intellectual, corresponding elite of the day but at the same time someone who was clearly literate, alert, and plugged-in to the times he lived in. What appeals to me about Mormonism -- speaking as an Nth-generation atheist -- is its rootedness in its time and place. Do all ATLs need turn into shock-and-awe spectacles? Perhaps some could simply contain ideas that did not take the particular turn or carry the same weight that our own did? But not be otherwise spectacular!!!(tm)? So, say Joseph Smith developed an interest (in any direction at all) with regard to the nascent labor movements, or spiritualist movements, of his age -- does it really have to change the entire universe? Bahh. Still interesting.
Ok. All that being said, I have entertained a vague ATL for a while. Smith hooks up with William Walker, somehow, however. He goes to Nicaragua with the fillibusteros. Where is soon discovered archeological proof (srsly!!!!) of the Book of Mormon's narrative. OTL unwinds spectactularly from there.
(And yes, I do keep Alex Cox's film Walker close here -- honestly, I think it's one of the most heartbreakingly American movies ever made, despite a British director and all-Nicaraguan-Mexican shooting.)