Paul's letters are important to Christianity, not so much because they preach a doctrine, though of course what he preaches has theological implications that we can and probably should parse, discuss, and understand. But his letters are more important because they preach the gospel.
It is a commonplace that the word gospel means "good news," but too seldom do we take that commonplace with sufficient seriousness. We don't understand it as an event in which divine good news is announced. Too often, instead, we take it to be a set of beliefs to which we are asked to subscribe. Or we take it to be a culture of which we should be a part. In either case we mistake the result or product of the good news for the news itself.
The good news is that God's kingdom is at hand (Mk. 1:15), not only something to wait for in the future, but something we are invited to make present and effective in our lives now. The gospel is the good news of our salvation (Eph. 1:13). In the Book of Mormon Jesus describes it this way:
Behold I have given you my gospel, and this is the gospel which I have given unto you—that I came into the world to do the will of my Father, because my Father sent me. And my Father sent me that I might be lifted up upon the cross; and after that I had been lifted up upon the cross, that I might draw all men unto me, that as I have been lifted up by men even so should men be lifted up by the Father, to stand before me, to be judged of their works, whether they be good or whether they be evil—and for this cause have I been lifted up; therefore, according to the power of the Father I will draw all men unto me, that they may be judged according to their works. And it shall come to pass, that whoso repenteth and is baptized in my name shall be filled; and if he endureth to the end, behold, him will I hold guiltless before my Father at that day when I shall stand to judge the world. (3 Ne. 27:13-16)
The gospel: Jesus was sent by the Father to do the Father's will. The Father's will was that he would be crucified in order to draw all men to him. He was lifted up on the cross: lifted up when he was crucified and lifted up when he was glorified in his resurrection. In the same way, and as a result, if we are willing to suffer with Christ (Rom. 8:17), then we too will be lifted up in glory.
Through Christ, the Father will judge us by our works. But if we have trusted in Jesus' crucifixion and resurrection, accepting his invitation through repentance and baptism and enduring in fidelity to him—in other words, through imitating Christ by doing the will of the Father—then the Father and the Son will judge us not-guilty. Fidelity to the gospel message means salvation.
I take it that is what we are told to preach when twice in the revelations of the Doctrine and Covenants we are told to say "nothing but repentance unto this generation" (D&C 6:9, 11:9). We are to announce the divine call of the gospel, the call to come to the person, Christ, and the way of being that he has made manifest in his life, death, and resurrection. As I understand it, therefore, the fullness of the gospel that we are told is given in the Book of Mormon (D&C 42:12; see also D&C 90:11) refers not so much to a complete understanding of doctrine as it does to the fullness of the gospel proclamation, the proclamation that Jesus makes in 3 Nephi.
Based on my experience, I think that when we receive that good news, we understand it as a call to take part in a life made manifest through Jesus. That call came to me in and through the Restoration of which the LDS Church is a divine effect. But after hearing the call and responding with "yes," it is easy for our life in the gospel to slip into only a relationship to doctrine and culture, to friends and family and leaders and habits and ideas. The Spirit accepted in the call can easily be elided or forgotten in the ossification of the doctrine, culture, practices, and relationships for which it is the motive.
The challenge, therefore, is to remain true and faithful to the call in our understanding of doctrine and our life with everything and everyone else.