I did not have a chance in commenting on this matter. BTW, Joseph-i asked the question rethorically, so as to stimulate discussion on this matter, which it did.
“onlyemes” wrote very accurately and completely about this issue. The “remo” that joseph quotes (orach chaim 88) actually brings down the minhag mentioned from the “hagohs maimaoni” them dismisses it ,relying upon rashi and then says (for himself), “aval haminhag bemedinos eilu kesvoro rishono (to prohibit this). “
On this ,the mishneh berurah counters and says ” ubemedinosainu nuhago hetter”. In other words, in the remo’s place, they tended to prohibit women from doing this in their days of ‘niddah” and in the mishneh berurah’s place, they allowed it.
There are other opinions that you wil lfind in the mishne berurah and other commentaires on the shulchan aruch- but what is absolutely clear is that it is NOT an issur-only a minhag. the halocho is clear “Kol hatemeim -afilu niddos- mutorim le’echoz besefer torah velikro bo” (joreh deah 282), just like “oomis’ said.
All this is based on the gemoro brochos “ein divrei torah mekablim tumah”, the rambam paskens the same way and, obviously, the “mechaber’ who paskens like the rsmbam. The Remo does not comment on that “mechaber” (joreh deah 282) at all, because the din is clear: women can hold a sefer torah at any time, even when the are “niddos’ (emphasis by the bais josef himself).
Whether to dance with the sefer torah would depend upon the minhag hamokom, the custom of the place.
I have difficulty accepting that Rav Soloveichink paskened as intimated. One, becausze many of hsi talmidim do differently and two, because to say -as indicated- that it is a minhag that should not be changed- well, it seems that there were many different minhagim on this for many centuries. So, it is werroneous to say that there was a singular minhag on this.
As far as the dancing goes, ‘onlyemes’ is absoluteyl right- it has nothing to do with “issur niddah’ and everything to do with the reluctance of present -day rabbonim (especially chareidi ones) to give women more of a voice and role in the shul. There surely is no issur on this.