I would say the WB is likely the biggest limitation I have found. It takes a minimum of 8 menu steps to set white balance underwater, and even then it's not ideal. Clearly on this dive I missed the white balance a bit -- it's something that will take some practice I think.
WB has it's place. I don't agree that you should 'fudge' the camera into reproducing colours that simply aren't visable at that given point.
I think the green murk really bring this film to life. Look at a lot of the movies that are out now, you'll notice that they colour grade them with the shadows being that murky-green colour, adds a lot of mood.
With this in mind, I don't think you should go out of your way to put reds back in when it really isn't necessary. I film caverns and the water is very blue/green, but that's the way it looks when you dive it, so that's the way I leave it. (plus I have lights, so WB would be a total train wreck.)
I can understand if you have fishes as your subject as people generally don't want to look at green fishes and corals, but for what you have done, I think it's spot on.
You can put reds back in when you get your lights, speaking of which, do you have any in mind? It'll be a challenge to fill the wide side of that lens with light.
Love your movie... put a narrative over it and it's on History channel!