If (as seems likely) the problem is caused by the fluorescent lighting cycling, it's not possible to "fix" it by adjusting WB - because you can't tell what part of the cycle the lights are going to be in for any given shot.
RAW of course helps in added flexibility of files but there is some factors that make it worse and some that lessen it. The light temperature varies with the cycle so the greatest impact is at high shutter speeds that are exposed only for a small sliver of degrees of a AC mains cycle. At high shutter speeds a narrower range of temperatures contributes to any given frame over a small portion of a cycle of peak towards Zero. It is just luck of which part of a cycle be the only light source, (unless a shutter synchronizer is set up which only allows the shutter to open at some specific time of a cycle) possibly at a very low output one frame and possibly at the peak output the next or anywhere in between. Slower shutter speeds will average out a continuously varying output level and temperature for the degrees of the cycle that contribute to the exposure so the color difference between any two random frames will be less. A 1/60(or 1/50) exposure would average out the peak and trough of the output as the output changes through 360 degrees of the cycle(4 peaks and 4 zero crossings). A 1/120 exposure would have 180 degrees from going between an arbitrary starting point, through the opposite and back to the starting point in a graph of output. A 1/240 would get an average between a peak and a trough regardless of where on the 1/4 cycle the exposure started. So this means that there is less variation in color for all speeds below 1/240 and a very great variation between random start points of say, 1/1000. For some subjects, AWB, with lower shutter speeds, can handle it nicely but in action sports expect much greater frame to frame variability when high shutter speeds are needed.. Stan St Petersburg Russia
>If (as seems likely) the problem is caused by the fluorescent >lighting cycling, it's not possible to "fix" it by >adjusting WB - because you can't tell what part of the cycle >the lights are going to be in for any given shot.
This is true for the older fixtures that use magnetic ballasts.
Bill stated they were different fixtures in each room and implied the one room didn't have any issues. I don't know if this is the case not knowing more information, but newer fixtures (especially in the US) use electronic ballasts that are not as problematic for photography. They run at thousands of cycles per second instead of cycling at line frequency making them virtually flicker free for general photography.