My 650D focuses fast enough in low light for stills with a bright (f2.0 or brighter) lens. But I can see how the AF would not track fast enough for video of (competition level) ballroom dancing. Unfortunately, I can't think of any way to improve video AF tracking speed. And I don't think even the new/updated 7D will be sufficient, AF video-wise.
My only recommendation is probably out of your budget, but I think a Panasonic AC90
would probably be able to get the shot(s) with its f1.5 lens combined with a smaller sensor to help keep things in focus (due to deeper DoF).
Or you could trick out your 650D for manual focus while shooting video
, but that's also an expensive proposition. (You'd probably also want to add an external monitor or loupe/Z-finder to that package to help nail focus at wide apertures.)