For what it's worth, a lot of the LDS religion is a time capsule of when it was founded, and the Curse of Ham is part of that. For example, the following is an 1834 commentary on the Bible by a doctor of divinity, printed in Baltimore by a Methodist Protestant church publisher:
http://books.google.com/books?id=l0wXAAAAYAAJ&pg=PA565&output=html
The footnote for Joshua 9:23:
The idea was so widespread that Charles Sumner, the abolitionist senator who suffered the curse of
cane, brought it up as an example of one of two main arguments for slavery in 1860:
http://books.google.com/books?id=Z-dAAAAAcAAJ&pg=PA112&output=html
The idea of American Indians being one of the lost tribes of Israel had been promoted as a (supposedly) scientific theory of origin by James Adair in the late 18th century and was of widespread interest and speculation into the early 19th. A good summary:
http://americancreation.blogspot.com/2008/07/native-americans-and-lost-tribes-of.html
The Word of Wisdom mimicked current health advice, which explains the curious phrase "hot drinks," which was common then. For example, the following was published by Anthony F. M. Willich, London, 1802, whose advice spread and flourished in America thanks to Sylvester Graham and other similar writers and lecturers:
http://books.google.com/books?id=VJ5bAAAAMAAJ&pg=PA85&output=html
Others in the thread have mentioned the strong influence of Masonic rituals on the church ceremonies.
Polygamy, the one practice that made the church stand out, was actually condemned in the Book of Mormon and seems to be a new development that became useful when Joseph Smith and others wanted it.
Jacob Cochrane had already tried to start a polygamous sect, but the 1840s was a time when many experiments involving unusual marriages were going on.
From a modern book about the "free love" Oneida Community which discusses the era a little:
http://books.google.com/books?id=b2SnVuHWIJkC&pg=PR9&output=html
So most of the church beliefs seem to be a mixture of what someone might come up with by taking the latest, newest ideas that looked like they were going to be eternal truths in the early 19th century--which of course is what Smith did. They're already starting to get dated, lose their social context and sound strange or inexplicable, since that era is long gone. But it would be like starting a church today, saying that God recommended a low-carb diet, accepted gay marriage and revealed that we once interbred with Neandertals--all revelations that would sound up-to-date to people in the early 21st century, just as Smith's revelations did to people in his day.