Mate... f2,8 is just a step away from f 4 so i doubt you will find your solution there....you can of course try.. but gotta say from my own experience that i've used my Tammy 28-75 f2,8 in all sorts of lighting conditions and usually in normal lit indoors ISO tends to go up while i find myself shooting f2,8 mostly....
In a theater type of lighting you'll be forced to use high ISO, medium shutter speed (like 1/40 or so, wich for dance isn't optimum) and f2,8...
The only solution that'll let you freeze movement in dance and that'll let you control the lighting instead of coping with it is one or several flashes.
I would try to poke around to see if they'll let you put some lighting on stage (off camera lighting with radio triggers)...for the price of a 50-135 (as recomended above) you can get yourself some studio strobes with modifyers (mmm maybe a 3 strobe kit of elinchrome Bx 500ri with some modifyers...they have here almost the same price as the lens...or you can get 4 Dlite it 4 to go, or 3 with some extra cool modifyers). Or you can go the cheaper way of getting some second hand speedlites and modifyers (the nikon sb 28 can be bought at a reasonable price and they are feature packed).
Then just practice, practice, get some lighting DVDs (lighting in layers, the strobist seminars or Zach Arias' one light workshop are great sources of knowledge
).
If you get to convince the school that you'll share with them the best shots for them to use as they see fit you can get yourself a wonderfull oportunity (and you can always figure out a lighting that will not bother so much the dancers and create some dramatic and theatrical images
.)
Good luck...and if you decide to go with the faster lenses bear in mind that the more luminous the shallower the depth of field will be, wich will create some focusing issues (and the lack of microadjustment on your kx can turn a pain in the ass the finding of a precise copy of a fast autofocus lens).
Oh and 3,5 will definitely not be enough if your f4 lens is already struggling there.
(And catch in focus as stated above is a good recomendation...for me it hasn't worked probably because of my own inability and impacience, lots of lost shots, but there's people who use it succesfully
).