When Jesus talked about a "kingdom", he talked about the same kingdom mentioned in Daniel 2:44: "And in the days of these kings shall the God of heaven set up a kingdom, which shall never be destroyed..., it shall break in pieces and consume all these kingdoms, and it shall stand forever." When Daniel says "all these kingdoms", he is referring to the man-made kingdoms he just described, as pictured by that multi-substance statue. These man-made kingdoms, or governments, as we call them today, consisted of a head of state and it's supporting government structure. When Daniel prophecied that these would be "broken in pieces" and be replaced by a kingdom set up by the "God of heaven", it is fair to assume that God's kingdom would also have a head of state (Jesus) and a supporting government structure run by ministers of various government departments/offices.(144,000) Otherwise it would not be a true replacement.
So, when Jesus told Pilate: "My kingdom is not of this world: then would my servants fight,...", he basically told Pilate, that he is not a king of a man-made government, "... but now is my kingdom not from hence (this world)." When Jesus promised his apostles that he would prepare a place for them (John 14:2), he obviously meant heaven, because that's where he went after he died on earth. And that's where the seat of his government or kingdom is located.
So, that's how JWs understand John 18:36.
In regards to your other comments: You are right about our belief that only a limited number (144,000 - Rev. 7:4; 14:1) will be in heaven to form that government. And that makes sense, because they have to rule over someone. That's where the earth and mankind comes in. We don't view this as "only a chance in the best case". There is nothing wrong with being human. Jehovah put a lot of thought into creating this earth for humans to enjoy. There were already millions of angels in heaven before Adam and Eve were created. If God wanted more angels in heaven, he could've created more. But He chose to create something new: humans. He didn't put them into a "utopian kingdom", as you put it, but it was called a paradise. This paradise was not a state of mind control, where man was to blindly follow orders, without the ability to reason. Jehovah also dignified man by giving him privacy and the freedom to choose. This paradise was to be eternal. Only by willfully doing wrong, would that eternity be lost. And it was lost, for Adam and Eve (Gen. 2:16,17).
It is, again, reasonable to conclude, though, that eternity for mankind is not lost forever. As an illustration: Would you spend a lot of time and thought to build a sail boat and never put it out to sea? Well, the full potential of this created earth has never been realised, and if it never would be, God's purpose could be called a failure. And why should He let that happen.
So, JWs believe that both heaven and earth are inhabited by beings created by God. They are different, but both are created in God's image, with their own specific eternal purpose.
Hope this helps a bit.