Matt, the simple answer to your question on Romans 11:6 is that you have to make some finer distinctions than you are accustomed to. Works are not in any way the ground of our justification, but are works entirely independent of our justification? Not at all, as I will attempt to show.
God’s election is without any merit on our part. Therefore, works are not a prior cause to the grace of justification. Therefore, St. Paul says,
For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast. For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them. (Ephesians 2:8-10)
This is what he is saying: Salvation is by grace, a free gift, totally unmerited on our part. We are saved through faith, which is also an unmerited gift of God and not given because of our works. Furthermore, we have no reason for boasting in our works because all our good works are dependent on God’s grace.
However, good works are necessary for salvation, not as if Christ’s merits were lacking in anything, but because it is necessary to be conformed to his image. St. Paul says, also in Romans,
Or despisest thou the riches of his goodness and forbearance and longsuffering; not knowing that the goodness of God leadeth thee to repentance? But after thy hardness and impenitent heart treasurest up unto thyself wrath against the day of wrath and revelation of the righteous judgment of God; Who will render to every man according to his deeds: To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life: But unto them that are contentious, and do not obey the truth, but obey unrighteousness, indignation and wrath. (Romans 2:4-8)
You see that St. Paul says that we will be judged according to our works, and this not a cherry on top as some suppose, but in reference to the final judgment. Heaven is for those who patiently continue in well doing. Hell is for those who do evil.
Mortal sin is also an important concept to understand because some mistakenly believe that once we receive the grace of justification, our salvation is assured apart from anything we do. St. Paul assures us that this false in Hebrews.
Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience, and our bodies washed with pure water. Let us hold fast the profession of our faith without wavering; (for he is faithful that promised;) And let us consider one another to provoke unto love and to good works: Not forsaking the assembling of ourselves together, as the manner of some is; but exhorting one another: and so much the more, as ye see the day approaching. For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins, But a certain fearful looking for of judgment and fiery indignation, which shall devour the adversaries. He that despised Moses’ law died without mercy under two or three witnesses: Of how much sorer punishment, suppose ye, shall he be thought worthy, who hath trodden under foot the Son of God, and hath counted the blood of the covenant, wherewith he was sanctified, an unholy thing, and hath done despite unto the Spirit of grace? For we know him that hath said, Vengeance belongeth unto me, I will recompense, saith the Lord. And again, The Lord shall judge his people. It is a fearful thing to fall into the hands of the living God. (Hebrews 10:22-31)
I would encourage you to read through all the letters of St. Paul (yes, that includes Hebrews) and look hard for places which seem to affirm or deny that salvation can be lost. Then think critically and decide which has the stronger case.