Here's a challenge: come up with a scenario where Mormonism is so widespread that it is comparable to modern, OTL Protestantism/Catholicism/Islam.
Your oldest possible PoD must still be within Joseph Smith Jr.'s life.
I don't think any OTL religions has achieved anything close to that level of growth you're talking about. Islam expanded geographically very rapidly, but it took a lot longer to get actual adherents.
One crazy thought: make the Taiping succeed in keeping at least part of China. I suspect that Mormon beliefs and Taiping belief can be made compatible easier than Taiping belief and traditional Christian belief--so thread the historical needle to have some kind of rappochement and doctrinal sorting out between the Taiping and the Mormons. Then have the Taiping pull a Meiji, which I think they are extremely apt to do. Bingo, a huge number of Chinese will be Mormon, with more becoming Mormon over time. Plus, Mormonism is now the successful model for native resistance to colonialism, so you might get Mormon movements elsewhere in Asia, in Africa, and even among Indians in Latin America (we Mormons would LOVE this last part). By the last half of the 20th Century, Mormonism is now, say, 5 to 6% of the world's population, several hundred million strong and still growing. That compares pretty well to the OTL Catholic percentage (17%), Protestants ( 9 - 10%), or Islam, (23%), or at least it puts Mormonism in the same conversation.
However, while this worldwide Mormonism is recognizably Mormon, its going to be different from OTL Mormonism in significant ways. Its not going to be run out of Salt Lake. It will be a worldwide religion but not a worldwide church. Successful Taiping are not going to take directions from to an American Westerner prophet and vice versa, probably not even formally. I think a modus vivendi that looks a lot like Eastern Orthodoxy could result, in which each culture or nation has its own Mormon church. The doctrinal basis for this would be (1) the fact that the Book of Mormon has a separate church organization and even a separate set of apostles for the New World, (2) the many references in Mormon scripture to the Father and the Son having separate dealings with the scattered peoples of the world, (3) Mormonism's doctrinal flexibility and pragmatism, (4) the fact that Mormons have always emphasized the need for modern prophets who can deliver God's message tailored to modern circumstances can develop nicely into a belief that each nation, culture, civilizational area, whatever, needs its own prophet who can tailor God's message for it, (5) the somewhat flexible hierarchical arrangments in the Bible, where there are multiple prophets from different areas, and in the Book of Mormon, where you have an outsider like Alma setting up a church organization that the ultimate insider (the Nephite King) goes along even though he apparently has significant religious authority himself, etc.
The American Mormon church probably retains some first among equals status, but conflicts of authority are likely. This much more widespread Mormonism is also a Mormonism that is going to contend more with schism, mutual excommunication, and all that sorry stuff.
BTW, what's with all the Mormon threads lately. I mean, Hail to the Prophet and all, but is there a reason for it?
Edit: We had some Taiping-Mormonism discussion in an earlier thread starting here:
https://www.alternatehistory.com/discussion/showpost.php?p=2120471&postcount=16