I shoot indoor skating events with even worse lighting than you're working with, so I understand your frustration, TOTALLY!
Here is my suggestion.
1. - based on the shot you posted, if you rented a 70-200/2.8"L" lens, you would be able to shoot in "Manual" set the apeture to 2.8 and your shutter speed to 1/250 at 1600 and stop the action with the same exposure you have on that shot. By shooting in manual, your shots will be consistantly exposed. I would also work in RAW format, but make sure you know how to open your photos in raw and work with them. Raw will give you some room to work if the shots are underexposed at all.
One disadvantage to your lens is that when you are zoomed in, the amount of light is decreased, so your apeture has to close. Lenses, such as the 70-200/2.8"L" stay at the same apeture at any distance.
2. - Make sure you are using AIservo mode in your AF. Using only ONE focus point, and that will make the focus follow the action, or track a moving player.
3. - Move the focus off of the shutter button to the *button to be used with your thumb. That is done by going into your custom functions and choosing #4, I think option 1. So you focus with your thumb, keep the focusing on while you aim at one person, then keep holding it while you press the shutter.
it will take you about 30 minutes of shooting this way before you decide you never want to go back.
hope this helps.
