A couple follow-up points:
Greg - Sadly you'll always have several shots with color cast in them. Completely unavoidable. But using the slower speed will get you a better average temp so hopefully you'll have less swing in temperature and more shots will be close enough in color temp.
Also in regards to auto ISO. One challenge with auto anything is that you're allowing the camera's metering to determine part of the exposure. You can often find that jersey color or background colors will adversely impact exposure that way. Try it out at your next game - take a shot as tight as possible on home player and do the same on visiting player. I don't have auto-ISO so not entirely sure how thesholds work with it. But see if jersey colors don't swing your exposures.
In a way that is a bit of an asside though. For the OPs shooting - a martial arts tournament or exhibition, they're not going to be following action for the length of the gym. It's more a matter of when they switch locations within the gym they need to re-evaluate exposure settings.
To the OP - what I mean by adjusting exposure is - as I mentioned here, uniform colors and background colors will adversely affect the exposure if you let the camera decide what exposure values to use. SO, take the camera's metering out of it. Here's a simple way to start:
- After you set the WB, Set camera to aperture priority.
- Select ISO 3200.
- Select widest aperture value you have available for your lens
- Take a test shot of a competitor under the lighting of the gym floor. Shoot tightly - as close to a head and shoulder portrait shot as you can get.
- review the photo on the LCD. If the face is too dark, dial in positive Exposure Compensation (read manual for how to do this - I cant say as I don't have your camera). If the face is too light, dial in negative exposure compensation
- Repeat step 4-5 until the face looks good
- Note what the aperture and shutter speed values are.
- switch the camera to manual exposure and set aperture and shutter speed values to values you got from above.
Now, the only thing you need to do is review shots periodically - especially when you switch to shooting a different area of the gym. Now that you're in manual, you simply adjust the shutter speed up or down to compensate for more or less light in new shooting position.