I am now going to write a new way how it was, but please note, that I am not paskening halacha lima'aseh, where you could go on Har Habayis and where you can't, and you shouldn't go on Har Habayis at all, as said by most Poskim, that we should not go on Har Habayis.
The first thing we need to do is figure out where the Kodesh HaKodoshim was. We know that the Rambam went onto Har Habayis, so it must be that in the Rambam's times they knew exactly where the Beis Hamikdash was. R' Binyamin from Toledo, who lived the same time as the Rambam, writes (26 אוצר מסעות עמוד) that in Yerushalayim there is a church called Templum Domini, (that is what The Dome of the Rock was called when the crusaders ruled Yerushalayim), which is the place of the Beis Hamikdash, and Omar built a big dome over there. This could prove that The Dome of the Rock is the place of the Beis Hamikdash. Although you could say he means Mizbeach, since until two hundred years ago, almost everybody who dealt with this question, said that The Dome of the Rock is the place of the Kodesh Hakodoshim, that is most probably where it was.
I have added a new video of the Lishkos on the northern side of the first Beis Hamikdash..
My name is Mendel Lewis.
Hashem said to Yechezkel, "Its reading in the Torah is as great as its building. Go and say it to them, and they will occupy themselves to read the form of it in the Torah. And in reward for its reading, that they occupy themselves to read about it, I count it for them as if they were occupied with the building of it. (Tanchuma tzav 14)