And I agree with pretty much all you said.
One thing I might just comment on would be...
...in which I would point out that there was not just an Old Testament Systems, but systems. I think that is an important distinction. Secondly, the Writer of Hebrews tells his Hebrew brethren to "go on unto perfection (and in view is the contrast between the incomplete nature of the Covenant of Law, and the completion our Author and Finisher/Completer brings)" which is something we have to carefully consider. Many have, due to the extremes that are arrived due to debates in the Body, embraced an antinomian position which essentially casts the Covenant of Law in a bad light. But the Law was good, the failure being on the part of men, who failed to keep it (Galatians 3:21).
So what we see happen is, in my view, a process which has distinct relevance to Atonement, and then to Reconciliation, though we do not separate these two, or, in other words, we don't have one without the other.
The basic point being that the penalty of sin is atoned for in the Work of the Cross. This made what follows, Reconciliation, whereby we are indwelt of God possible.
God bless.