Rejoining this discussion, allow me to make a few points.
It is patently clear from the gemoro sukkos that the balcony was not present for long stretches of the SECOND Bayis (and none in the first Bayis) and this makes R”moshe’s zz’l contention that it is d’oraisa even more problematic. I don’t know how R”moshe answers this question.
As for Sam2’s pointing out that R”Moshe zz’l holds that anything relating to “kedushah” needs a mechitza = this brings a plethora of questions, not the least that at R”moshe’s zz’l sons’ weddings, the seating was mixed (as attested by many).
Adding to this imbroglio about “kol isha”, Rav Weinberg zz’l held that “trei kole lo mishtamei”, two voices cannot be distinguished and, therefore, we can hear many women singing in unison. That would make the matter of Miriam and the women “because of kol isha” not possible.
I still have a gut feeling that, for long stretches of time, the shuls had separation of sexes but no mechitza, thereby respecting the “novih” and the gemoro sukkos that only required the balcony during yom tov. The architecture of the early shuls in europe tend to support that- a balcony was enough as long as there was separation.