The challenge, have the "new religions" and heretical movements of the 19th century become so powerful and successful that they essentially define that century as a "century of new religions", (perhaps even a "Year of New Religions" could occur). The rise of such religions as Mormonism, Babism, the Taiping version of Christianity, the Japanese Shinkōshūkyō and the Donghak in Korea should be so important that the 18th century is seen as a time similar to the sudden emergence of Islam and as important to subsequent historical developments as the French Revolution or the Fall of Rome. New religions and new heretical versions of old religions should be as disseminated as widely as possible, becoming state religions or the majority of the population in a wide variety of countries.
John Smith, Siyyid `Alí Muḥammad Shírází, Hong Xiuquan and Choe Je-u are seen as prophets and religious figures of equal stature to Jesus, Buddha and Muhammad. Any other "new religions" you know of you can throw into the deal give you significant bonus points.
The easiest point of departure for a larger Mormonism is a point of departure that eases the strained relationship Emma Smith had with Brigham Young. With such a point of departure the largest splinter group formed after Joseph Smith's death would not exist, giving the LDS church more people to work with to spread the message.
To kind of illustrate what I mean: Both the LDS Church and the RLDS Church hit the one million member mark at the same time. Shortly after this milestone was reached the RLDS church hit a spot of financial trouble and modified core doctrine so they could receive a lone from a Christian financial agency. This decision marked the end of the RLDS (who also changed their name to the Community of Christ) Church's growth, and began their steady decline.
If the RLDS had not split off then the LDS community would have hit the million member milestone much sooner; which could have resulted in the church achieving exponential growth sooner as well. So instead of having around 15 million members today, the church could of potentially had over 30 million members by now.
Such an increase in membership could also result in more states besides Utah being dominated by Mormon culture.
Another interesting place you could look for point of departures for a larger Mormon church is in various missions that were almost successful. When I say that I mean things like this:
In 1900 Mischa Markow preached in Bulgaria. His first few efforts at preaching LDS doctrine gathered large enough crowds that important individuals in the Bulgarian church tried to discredit him, which only made his sermons more popular. In the few short weeks he was preaching he became popular enough that the Bulgarian church felt that their only viable option was to have him arrested and expelled from the country. However, if my memory serves me correctly, Elder Markow almost succeeded in his efforts to appeal his expulsion.
That is all I have for you right now, I would have to take a closer look at the other movements you listed before I could say anything.