You are correct as to who are the covenant people of God. I appreciate your thoroughness and fidelity.
Paul mentions nothing of the word of God being written on our hearts and in our minds. We, as believers, are one with Christ in spirit, we are His body. We are beyond and higher in position to God than Israel has been or will be in the future. Our relationship to God is spiritual, not on earth, it is in the celestial realm, where He resides with His Beloved Son.
The law of God pertains to the earth. Perfect liberty is ours in Christ, and the law has no bearing on our relationship to God the Father. We are justified, glorified, and are seated among the celestial hosts, even now. There is no need for the law to be written on our hearts.
For those who dwell upon the earth during the Millennial age, such a quickening as will abide through supernatural writing of God upon the heart and mind of Israel, will be needed in that environment on earth. Sin will still be present, and death will not be done away with during that thousand year period.
Shalom, To the above I agree, everything else you wrote is simply not supported by the OT or the NT.