I agree with almost of all what you said except for your last statement, “Those are the works of a Christian and they are part of our salvation.”
A true Christian will bear fruit and will demonstrate love in action as you mentioned. I think we can all agree with that. There are too many people who have claimed to have said the “Sinner’s Prayer” but have never shown any evidence of an inward change of heart. I believe that is what James meant when he said faith without works is dead. If a person claims to be a Christian but their lifestyle doesn’t confirm that then it is likely they don’t really have a true faith.
Therefore, I would still argue that a true belief is what brings salvation to a person and not a combination of works or love in action. The good works are a response to salvation and demonstrate that a person has been truly regenerate as a new creature - born from above. The work of Jesus was sufficient to obtain our salvation; all we have to do is believe. But, if we do believe then all will know it by our actions.
This "failed to regenerate" argument is nonsense and a convenient talking point to avoid the real issues. When a man fails in his Christian walk, we simply say it was obvious that he was never a Christian to begin with... hogwash. God never made us into robots... we still have our free will. That free will also gives us the ability to reject our salvation. Don't forget that Lucifer made such a choice after being the brightest among the angels... and Adam made that choice to precipitate the Fall. Before those horrible choices, these beings were with God.