You mentioned a few issues, but I don't have time to deal with all of them.
But up front, do you find the 1689 Baptist confession to be so drastically opposed to the First London Confession?
Actually, if I understanding what you are getting at especially after the issue of NCT is the main topic. I am well aware that many people who hold to NCT say that the First London Confession is a NCT Confession, whereas the 1689 LBCF is a CT Confession.
I am not expert, but in recent years I have felt a need to study the Reformed Confessions. I think I can safely say that both the First and Second London Confessions are both based on CT.
NCT is a relatively new theology that attempts to bridge the gap between CT (both Baptist and Presbyterian) and Dispensationalism.
Perhaps I have only ran into a few fringe people who hold to NCT; however the ones I have run into have left me with a bad taste in my mouth. They said in language that was not open for discussion, that CT is basically heresy and although they did not want it on me; but that is the bottom line with them.
Please do not misunderstand me, I am not saying there is there are not differences between the CT that comes from the WCF and the First and Second London Baptist Confession, but that is a different matter.
By the way, although I hold to the 1689 LBCF, I have tremendous respect for Paedo-Baptist Confessions such as the WCF. In fact, RC Sproul was my favorite theologian.
By the way. "Progressive Christianity" should not be misunderstood to be NCT. Progressive Christianity is actually a very liberal movement that uses the Bible, but divorces itself from traditional Christianity on issues such as abortion, LBGQT+ and other issues. They use Liberal commentators to show that passages like Romans chapter one, has nothing to do with "homosexuality".
I am providing you a link in case you are interested concerning the 8 points of Progressive Christianity. https://progressivechristianity.org/the-8-points/