Now that I know a bit more, I will play with shutter speeds and see if it goes away (although I lose the ability to freeze).
In the US frequencies are 60hz (cycles). In Europe and the Middle-east it is 50hz (cycles) - others from various countries can/should confirm. If you're in an area with 60hz, use shutterspeeds which are multiples of 60 (1/60, 1/120, etc.) For 50hz, naturally use multiples of 50 (or as close as you can.) So you can still use fast shutterspeeds - just use one that is a multiple of the frequency. This will alleviate banding, but it will not alleviate strange colors from frame to frame. This is a problem with many different types of Gymnasium lighting - not just fluorescent. Banding is difficult to manage in post, but color casts can be addressed using WB and/or hue adjustments.