What you have is something that's accepted as "fact", but where is the cooborative evidence?
This happens to be why archaeology is so important when it comes to Temple Mount. If a Temple is to be built, we need to know if this really is the site, and not just something accepted as the site.
The Holy of Holies was visible to the people from the Mount of Olives through the EASTERN GATE (Golden Gate) if all the gates in the temple were opened. The ONLY PLACE THAT THIS COULD BE SEEN IS IF THE TEMPLE WAS BUILT ON TOP OF WHAT IS NOW CALLED THE DOME OF THE SPIRITS WHICH IS SOUTH OF THE DOME OF THE ROCK, which means that both Dome of the Rock and the Temple can exist at the same time, which the Bible, speaking of the Tribulation Temple, refers to as the Court of the Gentiles.
"If a Temple is to be built, we need to know if this really is the site, and not just something accepted as the site."
Though this is not a small matter, don't trip over it. The Jews have known exactly where the Temple should be built for a long long time.