I didn't disagree with any of your points. But they are a little simplistic and leave some important stuff out.
They are simplistic for the sake of focus.
Now I said I would be logical with this approach. So here is my point in so doing.
point 1 was the law shows sin by that which is good. That is simple for example thou shalt not steal is a good things to steal is to sin. apply the same for all 10 including the Sabbath commandment. To not keep the day is sin according to the law.
Point 2 the law is for both Jew and Gentile, Simple again that means that all 10 are for all people that includes the Sabbath.
Point 3 keeping the law is impossible for slaves to the law of sin. that is a problem, If i can't keep the law then that is what shows me I need saving. Take note, its my inability to keep the law that shows I need saving. Saving from what? Form my inability to keep the law and thus my sin. So salvation must involve a process of where I am changed and enabled to keep the law.
It can not be any other way if logic is to be applied here. I break the the law which is sin. the law reveals that fact that I sin and break the law. I try to keep it and fail thus I find I need saving. So I am now looking for a saviour that can save me from sinning/breaking the law. I am looking for someone who can do for me what I can't do for myself. I am looking for someone who can cause me to keep the law somehow. Anything short of this is no salvation at all. If I am left breaking the law then I am still in sin and not saved. If the law is taken away it changes nothing as I am still sinning I just don't have writing telling me anymore.
Point 4, Christ happens to be the only one who has the ability to do the above. He not only forgives by his death, but he transforms by the power of His Resurrection. Thus in Christ I find exactly what I need, Mercy for the sins I have committed and freedom from committing sin in the future.
Point 5 is connected. It is indeed Sin/breaking the law that Jesus saves us from. Sin as well established,is breaking the law and thus to be saved from sin is to be saved from breaking the law. Thus there is only one logical conclusion based on the revelation of scripture.
Christ Jesus saves by transforming disobedient sinners to obedient saints so to speak. This absolutely has to include the Sabbath as the Sabbath day is given in the law sin not to keep it both to Jew and Gentile as you have confessed. Thus it is as binding on us as it was on Israel. Not as a law to earn salvation but as a reprover of sin and showing us our need of a saviour.
Anything less than being empower to be obedient to the law is not salvation at all because it does not address the problem.