>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.