Salvation by works in the Book of Mormon

Alma Chapter 5 [Book of Mormon]
What follows in quotes is not found in the Book of Mormon Proper but is a Chapter Summary found in the Book of Mormon published by the “Church of Jesus Christ of Latter-day Saints”. This means it is an official interpretation of this chapter, it is what the Church actually teaches, not just a private interpretation of the Book of Mormon.
“To gain salvation, men must repent and keep the commandments, be born again, cleanse their garments through the blood of Christ, be humble and strip themselves from pride and envy and do the works of righteousness…”
This bible verse comes to mind: I do not nullify the grace of God, for if justification were through the law, then Christ died for no purpose. (Galatians 2:21 (ESV)
And indeed in Mormon doctrine Christ died for no purpose. They are the original “Crossless Christianity” which is not Christianity at all. The above quoted portion from The Book of Mormon capitalizes on this. It is at total odds with the New Testament which is about the forgiveness of sins, and finding salvation in Christ, not in our works. In fact the message of the New Testament is that all of the above mentioned things are impossible for men to do. “Keep the Commandments” show me one who has and I’ll show you Jesus Christ or a hypocrite. Being “Born Again” is the work of the Holy Spirit, not us according to John 3. “Cleansing our garments in the blood of the lamb,” this hints at revelation, where those who come out of the great tribulation have cleansed their robes in the blood of the lamb. This is figurative language for what happens to us as we live through the tribulations of this world. “Be humble and strip ourselves of pride and envy” simple experience in the world ought to show this is impossible, but true repentance and humility is a gift of the Holy Spirit, Acts 11:18 (God Grants repentance) as for humility? “We love because he first loved us.” (1 John 4:19 (ESV) And it is this love that is not arrogant or rude, 1 Cor. 13:4-5. And even our most righteous works, our best works need the forgiveness of Christ to be truly good, because without Christ they are “filthy rags” (Isaiah 64:6).
In this Mormon doctrine is totally at odds with the scriptures of the New Testament which they claim also to believe. Salvation is by Grace through faith: For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, [9] not a result of works, so that no one may boast. (Ephes. 2:8-9 (ESV)