If you don't have a 70-200mm f/2.8L IS II USM, I would definitely consider it and take it for a test drive even. My experience, and I've had the 135 L and the 200mm f/2L IS USM (both now sold), is that the 70-200 II is faster to AF than the 200 f/2L. I know, because I used to use both exclusively to capture indoor ice skating. The 135mm could not keep up and many shots were missed because of it.
The zoom also allows for more shots. Especially when you need to be stationary and the action is going towards and away from you.
I sold my 200 f/2L IS and later on picked up a mint 200mm f/1.8L USM for half the price. That is one of the sharpest lenses ever and mostly because it had lead in the elements. Canon no longer produces elements with lead.
Sample taken with the 5D III at 200mm f/1.8 ISO640:
Here are some samples taken with the 200mm f/2L IS and 70-200mm f/2.8L IS II wide open and at 200mm:
5d II @ 200mm f/2 ISO160:
5D II @ 200mm f/2.8 ISO320:
Hope that this helps.