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That sounds like fun and a good opportunity to learn. Curious, what cameras do you and crew use UW and topside ?
When I worked for the NBA, we always shot full manual. When you are in the deep, the light is less but constant. You are not changing from situations where the light gets super bright and goes dark. I agree with what has been said. Shoot full manual. Here is what you have to ask yourself, "Self, do I want the machine doing all of the thinking, or do I want to do the thinking?" Auto is nice, but it is the lazy man's solution. Plus, you can tell a video shot in full auto!
I would try aperture 5.6, ISO 1250. Increase ISO or open aperture if it's too dark, decrease ISO if it's too bright.
Increasing ISO will add noise, opening the aperture will put more of the scene out of focus.
If you are happy with how your raw footage looks, but unhappy with what you see on Youtube, it is your editing render settings, Youtube's conversion, or both.
How does your raw footage and edited video look when played off your hard drive.
I think 1/500 is too fast a shutter speed for your video footage to look natural.
What is your camera video recording setting ? 24p 30p or 60p ? I suggest making your shutter speed 1/50, 1/60 or 1/120 depending on your recording setting.
I also think you should try manual white balance. Use the sand as your reference.