Fullness is a subjective term, except in cases where exact measurements can be made. It always will be. I am fine with using it as a general statement about a few core pillars, for example - but those core pillars are taught in the Bibke, as well.
I would agree that the core concepts we generally associate with the Gospel (faith in Jesus as the Savior and Redeemer, repentance, baptism, the Holy Guost, enduring to the end) are taught more clearly in the BofM than in the Bible, but exaltation isn't taught clearly, if at all, in the BofM. It is taught in the Bible - as one of the core themes, actually.
I believe acceptance of the BofM is to enable people to read the Bible with new eyes, so to speak, and see things that the Bible teaches that have not been recognized in traditional Christian theology - particularly those that deal with the individuality of God, the Father, and God, the Son, and our relationship to them. Those things are taught more directly in the Bible than in the BofM - and the BofM says explicitly one of its core purposes is to lead people to beleive the Bible (as opposed to what is taught about the Bible).
"Another" testimony of Jesus Christ presupposes an existing testimony of Jesus Christ - and what I just described is the way Joseph Smith and the early saints generally used the BofM. It was the cornerstone of their religion and testimonies of The Reatoration, but it wasn't the cornerstone of their Gospel study. That was the Bible.
I see through my glass, darkly - as I play my saxophone in harmony with the other instruments in God's orchestra. (h/t Elder Joseph Wirthlin)
Even if people view many things differently, the core Gospel principles (LOVE; belief in the unseen but hoped; self-reflective change; symbolic cleansing; striving to recognize the will of the divine; never giving up) are universal.
"For every complex problem there is an answer that is clear, simple, and wrong." H. L. Mencken