According to an article published by Rabbis Aryeh Frimer (Professor of Active Oxygen Chemistry at Bar Ilan University) and Dov Frimer (attorney and Adjunct Professor in Hebrew University) in Tradition(32:3, pp. 5-118, Winter 1998), Rav YB Soloveitchik, while willing to accommodate women’s prayer groups (although he later changed his mind), had a much more negative view of women dancing with the torah. While there is a chiyuv for women to pray, there is NO chiyuv for hakafos. Furthermore, Rav Soloveitchik would “unequivocally express his opposition to women’s hakafot”, and often “expressed his extreme annoyance at being cited as the authority who supposedly sanctioned women’s hakafot”.
So, in short:
1.Every other gadol clearly says “no” to women’s hakafos.
2. Even Rav YB Soloveitchik, supposedly the source for the heter of women’s hakafos, was against them.