Since I find the following statements by church leaders to be consistent with the host of scripture references on this topic, and they support my own conclusions on this issue, I will not here take the time to distinguish them, though I would expect those holding the opposite view to seek to do just that. Those holding the view that the will be progression between kingdoms should review these comments, check the sources, and compare the conclusions to the scriptures.
1. Joseph Smith (Teachings of the Prophet Joseph Smith, p.12)
“But except a man be born again, he cannot see the kingdom of God. This eternal truth settles the question of all men's religion. A man may be saved, after the judgment, in the terrestrial kingdom, or in the telestial kingdom, but he can never see the celestial kingdom of God, without being born of water and the Spirit. He may receive a glory like unto the moon, (i.e., of which the light of the moon is typical), or a star, (i.e., of which the light of the stars is typical), but he can never come unto Mount Zion, and unto the city of the living God, the heavenly Jerusalem, and to an innumerable company of angels; to the general assembly and church of the Firstborn, which are written in heaven, and to God the judge of all, and to the spirits of just men made perfect, and to Jesus the Mediator of the new covenant, unless he becomes as a little child, and is taught by the Spirit of God”
2. George Albert Smith (Conference Report, October 1945, p.172)
“There are some people who have supposed that if we are quickened telestial bodies that eventually, throughout the ages of eternity, we will continue to progress until we will find our place in the celestial kingdom, but the scriptures and revelations of God have said that those who are quickened telestial bodies cannot come where God and Christ dwell, worlds without end.”
3. Spencer W. Kimball (The Teachings of Spencer W. Kimball, p.50; The Miracle of Forgiveness, p.243-244)
“After a person has been assigned to his place in the kingdom, either in the telestial, the terrestrial, or the celestial, or to his exaltation, he will never advance from his assigned glory to another glory. That is eternal! That is why we must make our decisions early in life and why it is imperative that such decisions be right.”
4. Joseph Fielding Smith (Doctrines of Salvation, 2:31-32)
It has been asked if it is possible for one who inherits the telestial glory to advance in time to the celestial glory?
The answer to this question is, No!
The scriptures are clear on this point. Speaking of those who go to the telestial kingdom, the revelation says: "And they shall be servants of the Most High; but where God and Christ dwell they cannot come, worlds without end."
Notwithstanding this statement, those who do not comprehend the word of the Lord argue that while this is true, that they cannot go where God is "worlds without end," yet in time they will get where God was, but he will have gone on to other heights.
This is false reasoning, illogical, and creates mischief in making people think they may procrastinate their repentance, but in course of time they will reach exaltation in celestial glory.
Now let us see how faulty this reasoning is. If in time those who enter the telestial glory may progress till they reach the stage in which the celestial is in now -- then they are in celestial glory, are they not, even if the celestial has advanced? That being the case (I state this for the argument only, for it is not true), then they partake of all the blessings which are now celestial. That means that they become gods, have exaltation, gain the fulness of the Father, and receive a continuation of the "seeds forever." The Lord, however, has said that these blessings, which are celestial blessings, they may never have; they are barred forever!
The celestial and terrestrial and telestial glories, I have heard compared to the wheels on a train. The second and third may, and will, reach the place where the first was, but the first will have moved on and will still be just the same distance in advance of them. This illustration is not true! The wheels do not run on the same track, and do not go in the same direction. The terrestrial and the telestial are limited in their powers of advancement, worlds without end.
5. James E. Talmage (Conference Report, April 1930, p.96)
The Lord has told us of places prepared for those entitled to salvation. He has told us that those who will keep all the laws and commandments of God can come where he is and shall be heirs of celestial glory and power. And he has told us of lesser degrees unto which others who have failed to rise to the occasion of laying hold on the blessing of eternal life, in its fulness, shall come; and concerning the last of these kingdoms of glories, known to us as the Telestial, the Lord has said that it excels all that the human mind can conceive in glory, and yet the one in the Telestial Kingdom is condemned so far as his actions have rendered him incapable of attaining to the higher glories and blessings which mean power and advancement.
6. Bruce R. McConkie ("The Seven Deadly Heresies," Classic Speeches, Provo, UT: Brigham Young University, 1994, pp. 175-176) & (Doctrinal New Testament Com. 1: 196)
BYU: Heresy five: There are those who say that there is progression from one kingdom to another in the eternal worlds or that lower kingdoms eventually progress to where higher kingdoms once were.
This belief lulls men into a state of carnal security. It causes them to say, "God is so merciful; surely he will save us all eventually; if we do not gain the celestial kingdom now, eventually we will; so why worry?"
It lets people live a life of sin here and now with the hope that they will be saved eventually.
The true doctrine is that all men will be resurrected, but they will come forth in the resurrection with different kinds of bodies - some celestial, others terrestrial, others telestial, and some with bodies incapable of standing any degree of glory. The body we receive in the resurrection determines the glory we receive in the kingdoms that are prepared.
Of those in the telestial world it is written:
"And they shall be servants of the Most High, but where God and Christ dwell they cannot come, worlds without end" (D&C 76:112).
Of those who had the opportunity to enter into the new and everlasting covenant of marriage in this life and who did not do it the revelation says:.
Therefore, when they are out of the world they neither marry nor are given in marriage; but are appointed angels in heaven; which angels are ministering servants, to minister for those who are worthy of a far more, and an exceeding, and an eternal weight of glory.
For these angels did not abide my law; therefore, they cannot be enlarged, but remain separately and singly, without exaltation, in their saved condition, to all eternity; and from henceforth are not gods, but are angels of God forever and ever. [D&C 132:16-17]
They neither progress from one kingdom to another, nor does a lower kingdom ever get where a higher kingdom once was. Whatever eternal progression there is, it is within a sphere.
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DNT: It is from these revelations which recite that resurrected beings come forth with different kinds of bodies [D&C 76; D&C 88:16-33; 1 Cor 15:35-58] that we learn a few of the many revealed reasons why there is not and cannot be progression from one degree of glory to another after the resurrection.