There as been some misrepesentation of the halacha here. I hope to clear up a few things.
1. The minhag mentioned by and rejected by the Rema regarding women going to shul, seeing the sefer torah, and by the way, saying shem hashem (including all forms of davening, bentching also included)applies only to women while they are “ro’ot dam” and not when they are in shiva ne’ki’im or after. Therefore, this entire discussion has nothing to do with tum’as nidah or going to the mikveh. Married (mikveh going)and unmarried ( non-mikveh going)women are equal. To repeat, the Rema rejects this stringent opinion and permits women to daven, come to shul, see the sefer Torah, etc… at all times.
2. The Mishna Brurah quotes the Chayei Adam (and agrees with him) only regarding looking at the words of the Sefer Torah while it is lifted up in hagbah. This would also apply ONLY to women who are actively ro’ot dam.
3. Women who want to touch, kiss, or dance with the Sefer Torah do not see the letters , since the Sefer is always totally rolled and covered, and therefore, any alleged prohibition is misplaced.
4. Rabbonim who are not in favor of women dancing with the Torah do not do so because of nidah, as we have shown here. It is because of concerns relating to the women’s true intent, feminism, reform, etc… This of course is debatable, but has nothing to do with nidah.
5.The Mishnah Brurah mentions the minhag of a yoledet refraining from going to the cemetery until she is toveles. This also has nothing to do with tumah (the cemetery by definition is full of tumas ha’mes). Rather it is connected to kabbalistic ideas regarding mazikin and sheidim.
The bottom line is that issues of nidah for women dancing with the Sefer Torah are irrelevant.