Kasha,
You misrepresent Rav Henkin. He said it is permitted for women to dance in the same ROOM with men but not WITH men. Bnei Banim, vol. 1 no. 37 part 9.
Rav Henkin also has brought many sources that disagree with some of the strict opinions brought down by Rav Falk. I’d post more but it is getting close to Shabat.