This is an adjustment to my ponderings in my previous post. I hope to address my ponderings in detailed posts, but hey, it's complicated, right?
I had wondered how it was possible for Paul and the Gospel authors to use such similar technical language, such as "new covenant" in 1 Cor 14:24, a decade before the Gospels were written. In this particular case, ancient Scripture mentions the "covenant" with God repeatedly, then Jesus comes along and reworks the human understanding of a relationship with God. It was almost obvious to refer to this as a new covenant, to the extent that different writers might have invented the phrase independently.
For other phrases, there is an additional consideration. The authorship of the letters and epistles attributed to Paul is heavily debated. Without listing books here (easy enough to find even on Wikipedia), modern scholars agree that seven books were written or dictated by Paul himself, but the authorship and dating of the other six is heavily debated. If a follower of Paul actually wrote a letter and claimed it was from Paul, even in good faith, and if the letter was written a decade or two after Paul's undisputed letters, then the later authors would have been writing at the same time as the Gospel authors. If that's the case, the similar phraseology is more easily explained. To be clear, few modern scholars would claim that Paul himself unquestionably wrote all 13 letters.
This issue also raises a question of interpretation. Is an undisputed Pauline letter more authoritative than a disputed Pauline letter? In my opinion, yes. In particular, passages about women remaining silent are all disputed as to authorship. They were either written by someone else, or were intended to refer to common cultural practice and not to Paul's recommended practice.