The "true God" is Jesus. For a more detailed Hebraic view of God, pick up a copy of Margaret Barker's The Great Angel: A Study of Israel's Second God. The LDS view of the Godhead is that Jesus is Jehovah. When Adam sinned in the Garden of Eden, the Father (Elyon or Elohim) could no longer communicate with man directly, but needed an intercessor. That intercessor was Jehovah (YHWH). When the Earth is glorified and redeemed, Jehovah will return it to His Father, having fulfilled His stewardship. Jehovah is the supreme judge of both man and nations, but John informs us that the "Father judges no man, but has committed all judgment to the Son." Jehovah is the beginning and the end, while Jesus is the Alpha and Omega. Jehovah, in Zechariah, reports that the Jews will look upon "Me" who they had "pierced."
Thus, Jehovah and Jesus are one and the same.
As far as the "questionable accounts" of our archaeology, that's your call. The Jews and Muslims can reject anything they wish, as well.
Regarding the "immortal soul," the JWs have little to argue on as it's quite clear that the early "first century" Christians believed that human beings had spirits. Peter recounts: "For for this cause was the gospel preached also to them that are dead, that they might be judged according to men in the flesh, but live according to God in the spirit." (1 Peter 4:6) How can the gospel be preached to the dead who are living according to God in the spirit if they don't exist? And Peter also was conflicted. "For I am in a strait betwixt the two, having a desire to depart and to be with Christ...nevertheless to abide in the flesh is more needful for you." (Philippians 1:23-24) Paul, likewise, stated that he would "rather to be absent from th body and to be present with the Lord." Paul also knewa man "whither in the body...[or] "out of the body, I cannot tell." (2 Cor. 12:1-4) And the disciples asked the Lord, "Master, who did sin, this man or his parents that he was born blind?" Jesus never corrected them or said, "Ye do err not knowing the scriptures," he answered that neither sinned, but that the works of God should be manifest in him. In other words, they not only believed in man having a spirit; they believed that man lived prior to his earthly existence. Jerimiah was told by the Lord: "Before I formed thee in the belly I knew thee; and befor thou camest forth out of the womb I sanctified thee, and I ordained thee to be a prophet unto the nations." (Jerimiah 1:5) Not only did the Lord know him, but He ordained him to be a prophet.
The Watchtower and Awake! magazines both like to talk about the Bible "clearly" teaching this or that, but the immortality of man couldn't be any clearer than it is in the scriptures. All those "scriptures" from Ecclesiastes were written by a man who, if they were written by Solomon, came from a man who had fallen out of favor with God. He had introduced heathen worship into Israel through his idolatrous wives -- wives who were not given to him by God, but who were part of political treaties. His polemics had to do with philosophy ("under the sun"), not eschatology.
But you can believe as you wish.