The Gemara in Zevachim (54b) says that the Beis Hamikdash is higher than the whole Eretz Yisroel, except for Ein Eitam, which is twenty-three amos higher than the Azarah. However, there is a problem, because nowadays, the top of Har Habayis is 744 meters (2440 feet) above sea level, but all the mountains around it, like Har Hazeisim and Har Tziyon, are higher than that! Also, Ein Eitam, (as said in a previous post,) is 830 meters (2725 feet) above sea level, which is much more than twenty-three amos higher!
This question was asked to the Radvaz (שו"ת ח"ב סימן תרלט) and he answered that there are two reasons for this. Number one, the Goyim, because of their hate for the Yidden, destroyed the Bei Hamikdash completely, "they razed it down to its foundation", and also so it won't be higher than their holy place in Yerushalayim, and because it is a mountain, the rains would wash away the dirt, lowering it. Also, many non-Jewish kings dug to find the foundations, to build their own buildings on them. The second reason is that Yerushalayim used to be lower, but each time it was destroyed and rebuilt, they rebuilt it on top of the old ruins, making it higher.
It seems that the first reason would be the main reason, because based on the excavations in Yerushalayim, we get a picture of how high it was back than, and it is not that big of a difference.
Now we need to figure out how high it actually was. This is not that hard once you know the location of Ein Eitam, because the Azarah is twenty-three amos lower than it, 819 meters above sea level. Taking away a few meters because of the Radvaz's second reason, I would say it was about 815 meters above sea level.
Based on this, we could understand why Yosifun writes (wars 5:5:1) that the height of the walls of Har Habayis was 300 amos. Although Yosifun always exaggerates, if the height was only around 100 amos, like it is now, it doesn't make sense that he would exaggerate that much. However, based on what we said, the height of the walls of Har Habayis was 286 amos, and he is only adding 14 amos, which makes more sense.
Now, in the Letter of Aristeas, quoted in Tavnis Heichal and Seder Hadoros (ג'תקט"ו), it says that the Beis Hamikdash was surrounded by three walls which were over seventy amos high. The Tiferes Yisroel (in his explanation of his diagram of the Beis Hamikdash, #1) explains that he is talking about the walls of Har Habayis, which were all high, besides for the east wall, which was lower. In Kuntres Hamoded he explains that this is including the height of Har Habayis from street level, but the actual walls surrounding Har Habayis were only forty amos, like the Tosfos Yeshanim (Yoma 16a) writes. This seems to contradict what we just said. However, if you read the letter carefully, It says that the walls on top of the mountain were seventy amos, but it doesn't say the height of Har Habayis from street level. However, this does not mean that Aristeas is arguing with the Tosfos Yeshanim, because the Tavnis Heichal (2:2:15) writes that steps went up from the migrash to the actual (five hundred amah) Har Habayis, so we can say that the migrash was around thirty amos lower than the Har Habayis, and together with the forty amah high wall, the walls of the square Har Habayis were over seventy amos high, like Aristeas writes.
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)