So would you have two light lenses or one heavy lens?
A zoom is preferable if the action is ever coming toward or going away from you. On the sidelines, sometimes a prime lens is ok.
As for the AF of the 6D, I have written a lot on this already. With my own 135 f/2, I agree the AF speed is a bit slower than it should be (not as fast as with my 70-200 f/4). The reason seems to be, the AF sensor just isn't sophisticated enough to take advantage of a lens faster than f/4. All AF points other than the center point, can vary in their accuracy with my 135 f/2, and thus are unreliable...especially in servo mode. And the problem is, if you leave all points active, the camera always seems to want to find focus with any other point, instead of the better center point. With f/4 lenses, especially with the 70-200 f/4, this does not seem to be an issue at all.
This is obviously a "crippling" that was designed into the 6D, to keep 5D3 owners happy about paying $1200+ more, and to keep the parts cost of the 6D at rock bottom. If the 6D had a derivative of the 7D's AF sensor/system...5D3 owners would be a bit less happy...because the 6D's files are cleaner within a very usable ISO range, than are the 5D3's files...specifically the luminance noise.
My own experience in bright daylight with things like passing cars, is the servo AF on the 6D is generally much more accurate and faster, for objects coming toward the camera...than for objects receding quickly from the camera.
For indoor sports or other low light events where the targets stay close to the same distance from the camera, you can pretty much get accurate and adequately fast focus with most any fast aperture lens, and the 6D...especially if you only use center point in servo mode...or in single shot mode for that matter (with multiple half press to keep engaging and tweaking the focus).