I think part of the answer will turn on what sort of camera you'll be filming with.
Inside a cave, you have no ambient light to outcompete, so the strength of your lights is less crucial if you have a camera that can film clean video in low light (e.g. ISO 3200, 6400 or even 12800 if filming with something like the Sony A7S/A7SII). This is great, because it means you can run your lights at lower power and still get nice footage. For reef shots, a camera with high sensitivity won't help much because it'll be equally sensitive to the ambient light, and what you want to do is have your torches brighter than the ambient light in order to bring back the full spectrum of colors. So, for reef scenes, the more powerful your lights, the better.
Also keep in mind the inverse square law of illumination -- light intensity decreases proportionately with the square of the distance from the light source. What this means, in practice, is that no light will strongly illuminate objects very far away. Importantly, it also means that varying the distance to the object you're trying to illuminate will be more effective than increasing the power of the light source. 12k lumens may be 50% brighter than 8k lumens, but in terms of reach, you're only increasing the light's reach by around 22%. (In other words, the 12k lumen light will produce the same illumination at 1.22m away as the 8k light would produce at 1m away). I don't don't dive in caves, so I can't really opine about how much of a difference the stronger light would make from experience, but, based on the above, I would say there's diminishing returns to increasing light intensity if your goal is to illuminate more of the cave.
Regarding 82CRI vs 96CRI -- I haven't seen any specific tests done underwater. I've used some 70CRI lights in the past and use 90CRI lights currently. My impression is that the higher CRI lights tend to produce richer shades of red and yellow. Is it a major difference? I doubt someone could look at footage blindly and tell you if it was filmed with 82CRI lights or 96CRI lights, because there's so many other variables confounding the final result (strength of the lights relative to the strength of the ambient light, etc) Now, if you were comparing them side by side, you'd probably see a difference. Maybe. But even then you'd be confounding it because one light is stronger.
Once you add cyan filters, CRI goes out the window since by definition the cyan filters are stripping out the reds and the yellows. With cyan filters, neither light is going to have a particularly good CRI.
If you're still confused, to what I did -- get the Gates GT14 lights. 90CRI and 14000 lumens -- best of both worlds
That's really helpful information! Good point about the sensitivity of the camera. Unfortunately I am using an olympus OMD and a gopro for my video, not a high sensitivity monster like what you mentioned. I'll have to push some lumens to make things pretty!
VERY good point about the filters, though. I guess if I am considering using those, I might as well go for the higher lumens for the reef work, and worry less about the CRI. I'm also happy to hear that there probably isn't a major difference between the 82 and 96 CRI lights if they are not side by side. I would really like to make sure I am getting good lighting if I am dropping this much cash on lights, but let's be honest - I'm not paying my bills based on this video.
As much as I love your suggestion of getting the best of both worlds with the gates lights, they are just outside of my pricepoint. I really wish I could pull those off - they look awesome!
Anyway, thanks so much for all your input!