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Your frustrations are business as usual for indoor sports photography. Now you know why sports photographers get paid the big bucks.
Indoor sports are great for the first game of the season, as we give thanks that we are no longer freezing outside. Then it's back to cursing the idiots who purchase lighting for gyms and pools.
As mentioned above, getting there early and letting your equipment adapt to the ambient temp and humidity is important. Fast lenses help; depending in the size of the pool and shooting positions, the 200 f/2 or 135 f/2 can be great tools.
Set the wb in kelvin, rather than letting the camera waste time figuring out the shifting lights. You will still have shifts, but they will usually be less extreme. Shoot a burst on a grey card to get a starting point for correcting each color phase. Set a manual exposure and be sure not to underexpose, because the red/magenta phase puts out less light anyway.
Although it may not seem like it, you were lucky. As you move to higher levels in swimming, in short pools the swimmers may not even take a breath on some legs, further increasing the challenge. Otherwise, catching faces is just a question of observation and timing. Pay attention to your target's rhythm and watch their shoulders for the muscle movement that precedes lifting their head for a breath.