If the sources only say that we dance in front of the kallah, that is not necessarily a “mitzva tantz”. All Jews dance in front of the kallah, as the gemara says, “ketzaid merakdim lifnei hakalla, Beis Shammai omrim- Kallah k’maves”. (I had to throw in my joke, I’ve said that at sheva brachos.)
I thought the defining part of a mitzva tantz, is the holding the gartel, and the spelling out Hashem’s name with dancing. Now, if you can find that in the machzor vitri, then we can dicker.