Really, for this level of play, 1/400 to 1/500 should be plenty of speed, so that shouldn't be an issue. And even then, with a MkIIN you should be able to comfortly be able to shoot at 1/1250 or 1/1600. The differene in noise at those ISOs should be nominal from your old 20D. Honestly, the real issue here seems to be missed focus. On all these the focus point seems to be somewhere behind the intended subject. So I hate to say it... but I don't think a new lens is what you really need. Now if you just want one - go for it. But it will not be the main thing that will improve your shots. A couple of things I would look at is if you are using single point focus with AI-Servo, and if what speed you have your AF set at. You actually want it to be on slow so it doesn't jump to a new subject as fast when trying to track your subjects.
Other then that.... color balance and all that look to be pretty much as on as you'll get in an environment like this. Keep at it... you have the right stuff to do the job, and you have a great subject. It will come. These aren't the easiest conditions to shoot in, but it will all come together for ya. Cheers.