FWIW, I shoot loads of karate and once tried the nikon 70-200vr [same as is basically] and to be honest, made not a blind bit of difference to kumite or catching movement in kata. Helps a little for catching stances in kata and thats it. Might be horses for courses of course, but I personally found it not much use. The F2.8 will be far more useful, a camera that handles noise well, or good noise reduction software even better.
also, 55 is very short even even you can stand on edge of tatame all the time, a longer option might be worth considering.