Geo, I think you'll be quite happy sticking to no picture profile for your Grand Cayman trip. You can acquire very nice footage in this mode underwater.
The Cinegamma settings allow you a bit more control about how the camera records highlight and shadow information. Some of them will allow you to capture slightly more light-level gradations in the highlights or shadows areas of the image before those areas clip to pure white or pure black. That's the theory. It's not as much extra gradation as a log gamma curve (e.g. SLOG2 or SLOG3) would allow you to capture, but it's more than you get using the no picture profile settings. They also have the advantage of letting you use the Rec709 color space (which is the color space you'll be outputting your video in for TV/web use) rather than the SGAMUT color space that you're forced to use with SLOG. This means you won't have weird color shifts that you need to fix in post as you would with SLOG.
In practice, there's some disadvantages and things to consider:
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You need to post-process your footage to get the best out of it. Like with SLOG, you're squeezing more dynamic range into the same 8 bits of luminance data. The camera records all light levels from 0 - 255, with 0 being black and 255 being white. Cinnegamas and SLOG give you the option to try to squeeze in 10 or 12 stops of dynamic range into those 255 levels, rather then the roughly 8 stops you get with no picture profile. This will end up producing a video file that has less contrast initially. So to get the same "pop" you'll need to boost the contrast in post processing. No picture profile lets you use the video files as is, without this extra step, so it's a distinct advantage if you have tight deadlines or you don't want to spend loads of time color correcting the footage.
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You trade detail in the midtones for extra detail in the shadows/highlights. Because you're squeezing in more information into the same 255 levels, you'll get less levels to represent the midtones -- which is usually where your subject is. So instead of having 255 levels to describe the black-to-white gradation of a manta's belly, for example, with cinnegamas you'll only get, say, 128, because the other 128 are now being used to record the gradations in the shadows of the coral the manta is hovering over, and in the sunrays. These are details you would otherwise lose clipping. So by choosing a cinnegama or slog profile, you're basically choosing to emphasize detail in the highlights and shadows at the expense of midtone detail. Now, there may be scenes where this is the right choice, but, overall, I think it's rare that you need more than 8 stops to showcase the underwater world well. Do you really need that much detail in your sunbursts? Or in the shadows? Or would you rather use that data to make your main subject look better?
Personally, I'm ok with sacrificing a bit of detail in the highlights and shadows to get a picture with more contrast/pop with limited post-processing. Over the years, I've come to believe that a wide dynamic range is really not that important underwater, since we're often working with artificial light (strobes or torches) that fill in the details in the shadows. Does more dynamic range help? Sure it does, especially with careful post-processing to tone-map that dynamic range into the smaller space of you output format. But it has less visual impact than nice colors and nice contrast.
To give you guys a visual reference for what I'm talking about, here is a short video with two scenes shot using no picture profile, cinegamma 1, cinegamma 2, cinegamma 4 and slog2, in that order. I took this footage yesterday with the A7RII set to UAWB, depth 3m, midday, good visibility. SLOG2 footage is at ISO800, F11. Other footage is at ISO200, F11. No post-processing was done. I also thew in a shot at the end to show what WB: Sunny looks like by comparison to UAWB.
https://youtu.be/Ap84hmJ4gpQ
As you can see, it's not a huge difference between No PP and Cinegamma 1, 2 and 4. SLOG does show a big difference, but that's because of the SGAMUT color space messing everything up. If there's any colorists out there that want to play with the footage to see if you can make the Cinegammas or SLOG look nicer than no picture profile, I'm happy to share it. It's about 144MB in h.264 1080p. If someone can suggest a web host, I can even put up the original 4k files.
Andrei:
Thank you for posting these tests. This is the sort of thing I was hoping we could do. I must say that my personal, subjective impression is that no picture profile looks better than the Cinegammas -- precisely for the reasons you mention here. Underwater photography rather changes the rules from what the cinematographers are attempting to achieve above water. I have been studying post processing, and "delogging" sLog 2 and 3 footage in Premiere Pro. I am collecting LUTS. I bet you are too and I would be surprised if you are not already pretty good at doing these things and better than I. I would, however, enjoy trying to delog the slog 2 footage you have here, and color correcting it. If you send me your email address I will give you access to my drop box. I have set up an underwater folder to faciliate exactly what you are mentioning here. One fellow in England color corrected some of my erroneous footage, taken in Cozumel, when I was attempting to do custom white balance at about 70 feet, with this camera. Somehow it resulted in an awful magenta cast that could not be corrected. Hence, I started this topic.
I find sLog2 or 3 difficult to work with for other reasons. Here are some issues we can discuss in this group:
FOCUS: First, Is it harder to focus in sLog footage? I too use manual focus with a "prefocus" on the back of the camera, and yes I constantly refocus when necessary. But does the camera's prefocus ability differ in different color profiles? A subsidiary question is whether the use of the "gamma assist" function on the a7s II (not sure if they have it on the a7r II) affects the focus.
FACILITATION OF PHOTOGRAPHY. Next, one of the advantages to shooting in no picture profile is the ability to move back and forth between video and RAW photography. I can do this on the fly, in a second or two, by just pulling a different trigger on my Nauticam housing. My take on it is that I can't take RAW photos when camera is set to sLog. If that is true, then I have to switch picture profiles before taking the photograph. This takes much longer, and if the camera is finding it harder to focus, this really compounds things.
WHITE BALANCE. I can't take a custom white balance in sLog2 or sLog3. The camera simply refuses to do it. The big, big, big result of the discussion on this topic, for me, is that I have abandoned custom white balance for ambient light (which everyone told me to religiously use including the company which sold me the camera and the housing) in favor of underwater auto white balance, which the purists pooh-pooh. But this too raises an issue. Does underwater auto white balance work differently sLog 2 and 3 does it does without a picture profile, or with a cinegamma profile? I think the delogging experiment will help answer this question.
I am delighted that everyone is having fun discussing these issues. I will get back to people with the tests I am planning for my trip to Grand Cayman next week! That way people can make suggestions and corrections.
GLP
Setup ready 4 next week !!!

That is quite the setup! Much bigger than mine.
Does the dog actually use the camera, and how is he at diving? I bet it helps to have an assistant like that.