Ezra says Artaxerxes supported the opposition to rebuilding the city and said it could only resume on his say-so. The letter is undated. Was it early in his reign? All we know is that, apparently, because of Nehemiah's good standing at court (and God's intervention), in his 20th year Art. has a change of heart. It doesn't mean all the neighbors were happy about it, though.
What you're asserting is circular reasoning, based on the assumption that verses 6 to 23 are parenthetical.
Ezra 6:14 indicates nothing other than that Artaxerxes I (after Darius) was supportive of rebuilding work in Jerusalem.
If you're applying Ezra 4:12 to Artaxerxes I, then the arrival of Jews "from you to us" would best fit the timing of Ezra and others going to Jerusalem in the 7th year Artaxerxes I, which would require that the order to halt building would follow that. But that would plainly contradict the fact that Ezra had gone to Jerusalem after Artaxerxes I had given Ezra a letter specifically supporting them.
It would be odd for Ezra 4:12 to refer to Jews who arrived in Jerusalem over 70 years prior (from return of Jews in 538BCE until in or after the accession year of Artaxerxes I, 465 BCE), as would be the case if it is said to refer to some time prior to Ezra going to Jerusalem but during the reign of Artaxerxes.
The book of Esther presents Xerxes I as favourable toward the Jews, with no indication that he was the 'Ahasuerus' who prevented construction in Jerusalem either. It is unlikely that Persia would have a Jewish queen for several years, but that Artaxerxes I would be unfamiliar with the Jews, but would then quickly learn they were 'bad' from his 'investigation'.
It is therefore more logical that Ezra chapter 4 simply presents events in chronological order. Ezra 4:6-7 is consistent with complaints in fairly quick succession to two kings largely unfamiliar with the Jews during relatively brief reigns between those of Cyrus and Darius. Since Ahasuerus (Xerxes) and Artaxerxes are common throne names that are used alternately at various times in the Persian dynasty, it is not especially remarkable that the Bible writer might employ those names, even if erroneously.