“R’ Moshe writes (and proves) the obligation to have a mechitza is d’Oraisa. (O.C. 1, 39)”
That is really difficult, since (1) the obligation for tefillah b’tzibur is a d’rabbanan, and (2) for most of the history of the beit hamikdash there was no mechitzah. Rav Soloveitchik z’tz’l wrote that the mechitzah requirement is d’rabbanan.
“If there a balcony in Shearith Israel, R’ Moshe would be mattir.”
In the main upstairs beit knesset, the ezrat nashim is a balcony. In the small beit knesset on the main level, and in the lower level beit knesset used for Shabat services in the summer, there is no balcony but a ten tefachim mechitzah. The architecture is modeled on the famous Esnoga in Amsterdam.
“other than the mechitzah, most of these Jews are upstanding and halachicallly committed.”
Halachically committed Jews can follow halachic opinions that differ from Rav Moshe z’tz’l especially when it has backing from the gemara and from a long tradition and was supported by a contemporary posek of similar stature.