Did the Rambam enter Har Habayis? (updated)

   In a previous post, I tried bringing a proof that the dome of the rock is the place of the Kodesh Hakodoshim from the fact that the Rambam went onto Har Habayis. However, the Rambam does not state clearly that he went onto Har Habayis. He writes (quoted in Sefer Hacharedim מצוות התלויות בארץ פ"ג)  "on the fourth day of the month of Cheshvan... We left from Acco to go up to Yerushalayim, under danger, and I went into the great and holy house, and I davened there. This is usually explained to mean the Har Habayis, the place of the great and holy house of Hashem, however, it can also be referring to a Shul, especially a Shul next to Har Habayis,  so the Rambam can be referring to that.
  In Kovetz Ma'alin BaKodesh, issue 37, (pp 93) ר' אמיחי אליאש brings a letter from R' Avraham, the Rambam's son, where he says that the Rambam, when writing the Sefer Hamitzvos, might have held that someone who is Tamey from a corpse is not allowed to go on the whole Har Habayis, although when he wrote the Mishneh Torah, he changed his mind. Based on this, we see that the Rambam might have held at the time of his going to Yerushalayim, that no Tamey person can go on Har Habayis at all, so he for sure could not have gone onto it. (You can still say that the Rambam went onto the part of Har Habayis that was added by Hurdus, which is not holy, and the Rambam calculated the boundaries of the holy Har Habayis based on the dome of the rock, but there is no proof from this letter.)

   ​However, in the next issue of Ma'alin Bakodesh.  R' Azaryah Ariel brings the Rambam in Peirush Hamishnayos Keilim 1:8, (which was written before Sefer Hamitzvos, and after the Rambam was in Eretz Yisrael,) where he writes clearly that a someone who is Tamey from a corpse is allowed to go on the Har Habayis. Based on this, he says that originally the Rambam held you could go up if you are Tamey from a corpse, but at some point, between writing Peirush Hamishnayos and Sefer Hamitzvos, he changed his mind and held it is forbidden, and then later, when he wrote Mishneh Torah, he went back to his earlier opinion that it is allowed. (ר' אמיחי אליאש responds to R' Azaryah Ariel in that same issue of Ma'alin Bakodesh, and then R' Azaryah Ariel answers back,)