The whole gospel is grace. Everything is by grace. But here here is where we differ with the Evangelicals. There is the lesser law and the higher law. The lesser law deals with Justification by grace and not by works. This initial salvation or "rescue" is God condescending and snatching us from the jaws of death and hell. The "saved" by grace and not by works "lest we boast" is talking about our initial justification or rescue. I like to replace the word "saved" with "rescue" to clarify what Paul is taking about.
FREE FALL RESCUE
In another sense, all of us when we leave our eternal home and step into this fallen world; take a step off the cliff into spiritual free fall headed straight to hell. Whether we realize we are falling from a cliff or not, the ground is approaching. God is like an Eagle and dive bomb us and in his condescension match our position and speed, and tap us on the shoulder and inform us of our dreadful condition. We are promised that Christ will even bare us up on Eagles wings so that we can stop our free fall. But even though we are no longer falling, we are still a long way from where we started.
JUSTIFICATION (NO WORKS NECESSARY)
After Justification, Christ's righteousness is "imputed" to us and we are "called" clean such that we are enable to receive the holy ghost through the merits of Christ. But just because we are justified and "called" clean doesn't really mean we are clear and ready to return into the presence of the Father. Sure, Christ condescends and hangs out with sinners and publicans and accepts us how we are. But not the Father. The Father is the Man of Holiness, and he permits no unclean thing into his presence. This is why it is imperative to understand the distinctness between the Father and the Son.
HIGHER LAW, COVENANT, PRIESTHOOD
But now that the believer in Christ, can enjoy the presence of "a portion" of the Holy Ghost, if he allows it, the Holy Ghost will work within that person to purify them, and perfect them. This is the higher covenant and higher law and higher gospel. Remember that Paul said in Hebrews that the Levitical Priesthood didn't have the power to make one perfect. (sanctified).
Heb. 7: 11 If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need was there that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron?
SANCTIFICATION (LIFETIME OF WORKS REQUIRED)
And remember the words of Christ to the rich young man who asked what he needed to do to gain eternal life. After reviewing the law and confessing that he had kept the law since he was a boy. The young man asked "what lack I yet" Christ responded, "If thou wilt be perfect" (sanctified) then accept the law of Consecration. (Matt 19;21). So, here the young man had to make a choice, enter into a covenant, and keep that covenant in exchange for the promise of sanctification. Yes, its the power and grace of Christ that empowers the keeping of the covenant and blesses the keeper with the promised sanctification or eventual disposition never to do evil but to do good continually. However, there are a whole lot of consecrating works between here and there which may not end until the end of the Millennium when Christ presents the Sanctified Earth and His sanctified people on it, to His Father.
THE LDS MESSAGE
Unless a person understands the difference between Justification (called clean) and Sanctification (made clean), then I can see why the LDS message may seem peculiar. All LDS who have been baptized have already been rescued. LDS members have already been justified and enjoy the reception of the Holy Ghost. We are already "called clean" through the merits, and mercy, and grace of Jesus Christ. That is water under the bridge. Now the whole LDS message is focused on Sanctification and preparing to receive and keeping the Law of Consecration. The whole focus of the New Testament, Higher Covenant is about "trying a little harder to be a little better." The focus is not trying to save ourselves, or even meet God half way. The focus is on receiving and exercising the grace, spirit, and power that God has already extended to us, and then asking to be added upon--- Grace upon grace and not a fullness at first (John 1).
AFTER ALL WE CAN DO
Again, "Being saved by grace after all we can do" is not talking about meeting God half way or even taking one step toward God by our own power. Nephi is talking about why they bother to keep the Law of Moses knowing salvation is in Christ. But Christ gave the Law, so therefore, Nephi's conclusion is that they will receive what Christ has already given them (1sts) until the time that he gives more (2nds).
After we are Justified and Christ breaks our free fall descent and bares us up on eagles wings. We still have much work to do to get back to our heavenly home. We have lost a lot of altitude. Christ gives us wings to bare us home. Christ teaches us how to fly. Some will look up at the cliff from which we fell, and fix our gaze on a lower perch and settle for a lesser reward. Although, others who put our faith in Christ's flying lessons and the wings we have been given will diligently, persistently, patiently use those wings to return us home again into the presence of the Father from whence we came.