Faith without works is dead even at its inception. The kind of faith that comes from God is a faith that works by love. It is never ALONE.
I can see that you are a strong believer in "sola fide," a doctrine I taught for nearly 30 years. I no longer subscribe to this doctrine.
You don't know the difference between the object of faith and the nature of faith. Faith justifies no one, saves no one and never will. The ACT of faith justifies no one, saves no one and never will. Demons have faith and have works and they will never be saved.
It is the object of faith that justifies and this is made abundantly clear in Romans 3:24-26. - "faith IN his blood" and "beleiving IN Christ." The gospel REVEALS the righteousness of God found in Christ as the proper OBJECT of faith (Rm. 1:17).
Romans 3:27 gives you one of two alternatives of how anyone can be justified - not three or four but only two and then rules out one leaving only one true alternative.
1. The law of works
2. The law of faith
The law of works is stated in Romans 2:6 "according to his deeds." This is how the law of works justifies. However, Paul denies this "law" as a valid law for justifying anyone.
The law of faith is stated in Romans 3:24-26 as obtaining justification by simply the OBJECT of faith "faith IN his blood" and "believing IN Christ"
Therefore, if the "law of works" is elminated then that leaves justification by "the law of faith" ONLY or ALONE - thus justification by faith ALONE.