A good summary of the fall of Jerusalem, blow by blow, is http://www.livius.org/ja-jn/jewish_wars/jwar04.html . If you read the documentation I linked, you will find that the Temple was on a heavily fortified platform next to the Gihon Spring, at the extreme northern end of the City of David, the "Old Town". Both the Antonia Fortress as well as the City of David were on Mount Moriah, the elongated hill which runs North and South. So your evidence merely establishes the relative positions of Antonia and the Temple, which is not in dispute. The distance between them is. And it makes sense that Herod would not have built the Temple in extreme proximity to the Roman fortress Antonia, nor accepted the Romans to build it so near, whichever came first, since the Romans came to Judea with Herod the Great. The Temple was evidently built on a platform, as the topography of Mount Moriah does not lend itself to much choice in this matter.
Police arrest 18-year-old Palestinian suspected in Old City stabbing (Haaretz)
from the article: Likud urges Shas, Lieberman to quit gov't over PM's 'intention'