SeattleTruthSeeker it's clear you have a good understanding of the gospel and the scriptures. I understand your statement about the Kingdom of God. What you say it true the Kingdom of God does refer to the church. If we look at the writings of early church leaders(more specifically Joseph Smith) it we can see that the phrase "Kingdom of God" is used to describe the Church, God's Kingdom in the eternities, as well as some other meanings. In some cases it is also used to describe the political Kingdom of God.
The truth is Joseph Smith did indeed establich the Council of Fifty in 1844. The Official name of this government as revealed to Joseph Smith is: "The Kingdom of God and His Laws, with the Keys and power thereof, and judgment in the hands of his servants, Ahman Christ." The more official name of the Council was the Kingdom of God. However it was usually refered to as the Council of Fifty.
But the establishment of this Kingdom of God was in no way intended to replace or take authority in the religious Kingdom of God. There is a distinct seperation between the two Kingdoms. They both fulfill different roles. The religious Kingdom of God(and probably the more important) takes care of the salvation need of the people. The political Kingdom of God takes care of the legal needs of the people.
So I would agree with you that scripturally the phrase "Kingdom of God" refers to the religious organization. That would be the most common usage. However according to Joseph Smith and many other early church leaders the phrase "Kingdom of God"
also means a political organization. An organization seperate from the church organization.
I usually make the distinction by saying "political Kingdom of God." But this concept is difficult to understand for most people. I know that when I first heard about it it took alot of study before I finally understood it.
I'm glad you took the time to go out and research it. And I agree with what you've said. I get the feeling, though, from your post that you feel a group claiming there is a political Kingdom of God would undermine the religious Kingdom of God. The political Kingdom of God is not a way into Heaven. The politcial Kingdom of God offers no means of salvation. The political Kingdom of God offers a form of government that is based on and upholds righteous principles. It's laws are based on God's will, not on the will of unrighteous politicians.
Hopefully some of my ramblings have helped out. Here's a good reference that should help you out in your studies:
"It Seems Like Heaven Began on Earth"