While the concept that most people will receive, to some degree, eschatological salvation, is not explicated in the Book of Mormon as it is in D&C 76, there is clearly the doctrine in germ form.
In the New Testament, based on the work of the High Priest after the sacrifice was slaughtered (cf. Lev 16-17), Christ is said to intercede before the Father; examples include:
Who is he that condemneth? It is Christ that died, yea, rather, that is risen again, who is even at the right hand of God, who also maketh intercession for us. (Rom 8:34)
Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he liveth to make intercession for them. (Heb 7:25)
Other texts in the New Testament implicitly refer to Christ’s intercession, such as Acts 7:55-56 where Christ is standing (implying activity) on the right-hand of the Father and Rev 5:6 where Christ presents his sacrifice before the throne of God the Father. Furthermore, 1 John 2:1-2 explicitly declares that Jesus is a present ιλασμος (propitiation/atoning sacrifice) for God’s people, not just those who will be converted at a future stage.
In the Book of Mormon, we read that Christ intercedes for everyone on the basis of His universal atonement:
Wherefore, he is the firstfruits unto God, inasmuch as he shall make intercession for all the children of men; and they that believe in him shall be saved. And because of the intercession for all, all men come unto God; wherefore, they stand in the presence of him to be judged of him according to the truth and holiness which is in him. Wherefore, the ends of the law which the Holy One hath given, unto the inflicting of the punishment which is affixed, which punishment that is affixed is in opposition to that of the happiness which is affixed, to answer the ends of the atonement. (2 Nephi 2:9-10)
And thus God breaketh the bands of death, having gained the victory over death, giving the Son power to make intercession for the children of men. (Mosiah 15:8)
Because Christ intercedes for all men, he assures the application of the benefit of His atoning work to all men, so outside those who willfully reject Christ and "crucify to themselves the Son of God afresh" (Heb 6:6; cf. 10:26-29), all will be the recipients of some form of eschatological salvation and reward.
While the Nephite record is not as explicit as D&C 76, something Latter-day Saints should expect (cf. D&C 128:18), the later, developed doctrine clearly is implicit in the Book of Mormon.