Yep. Best lens to do the job is the 300mm f2.8L and 400mm f2.8L. Otherwise the 70-200mm f2.8L is a very good lens too. However if that is still too expensive, can check out the Sigma 70-200mm f2.8 OS and/or Tamron 70-200mm f2.8 VC. Couple with a 1.4x TC, you can still shoot the action very well.
I would recommend the f4L version of the 70-200mm but when adding a 1.4x TC, it will be f5.6 and depending on the lighting available, it might not be enough. Thus if you are using a f2.8 lens, then it should not be a problem even with a 1.4x TC added on.
So TS, there is no need to look to original lenses, sometime third party lenses are also great and value for money.