I've always thought that as corrupt and evil as the guy was he must certainly have kept the best part for his own real estate interests and stuck the temple (and it's contributors) with a secondary site.
When the Romans burned and tore down the entirity of Jerusalem we lost a lot of records that could have told us precisely where the Temple should go.
So, other than the New Sanhedran folks probably being heretics, what else did you wish to know.
Today when you visit Temple Mount and go in the mosque there's an stone there that was supposed to have been under the original altar. It has what seems to be a horses' hoof print in it ~ which is a piece of identity reflected in the Moslem tradition that Mohammad mounted up to Heaven at that point on his horse. I've always wondered if there's any sort of Biblical information that describes that stone as well as the hoofprint. Just haven't found it, but until the stone can be explained, I'm going to be very open to the arguments of those who claim "this ain't it".