I don’t think any of these verses are conclusive Andrew. In particular:
Ephesians doesn’t say that Gentiles are included in the commonwealth of Israel. It says that once they were excluded (under the law) from the commonwealth of Israel and foreigners to the covenants of the promise … But now “they have been brought near” (no mention of commonwealth or covenant).
The Hebrews verses are quoting Jeremiah 31, primarily to Jewish recipients of the letter. It would be especially relevant to remind them of their inclusion in the new covenant.
Otherwise I think the verses you quote don’t seem particularly to reinforce your case. I don’t see the relevance of Romans 9-11, Galatians is ambiguous at best, and the names and gates of the New Jerusalem, whilst declaring a fulfilment for Israel, aren’t saying that only restored Israel may enter.
All these verses would be true of a fulfilment in which Israel as a nation was destroyed. They don’t speak of a continuing restored Israel.
I don’t see this vision of a restored Israel being declared by Jesus - rather warnings of the opposite, repeatedly.
Where else is there a vision of restored Israel, which you say “essentially runs through the whole New Testament”?