AnnOMaly:
True, 1 Esd. 2:18 adds "of the temple" when talking about the foundations, but Ezra 4:12 is the earlier version upon which the later Greek Esdras was based. Josephus' beliefs may well have relied on those later traditions. As you said earlier:
It has not been conclusively established that Ezra is the older version. And even if 1 Esdras came after, it was obviously understood then that the 'foundations' at Ezra 4:12 referred to the foundations of the temple. It's never specified as the foundations of anything other than the temple.
So, while it's interesting that Josephus took Ezra's 'Ahasuerus' to be Cambyses, it doesn't mean Josephus was correct.
Antiquities is a mix of history he gets right (and approximately right) and history he gets jumbled. If what he says can be corroborated elsewhere - especially independently - then we're on to a winner. Otherwise I'm a little more cautious.
Actually, Josephus took Ezra's 'Artaxerxes' to be Cambyses, which is indeed probably in error, but still in the correct period, prior to Darius. Ezra's 'Artaxerxes' - the recipient of the letter - would more likely refer to Bardiya, after complaints were sent to Ezra's 'Ahasuerus', who would more logically refer to Cambyses.