That's a shame - I just had another go at this with Hot4D, and am getting much better results now on a cube ! Or rather I was, until you said that you'd have to fly over a ton of ocean first :)
But, in case it helps this is what you get if you apply Hot4D to a cube, and give it tons of resolution on X and Z, and none on Y.... it animates perfectly, as long as you can't see the bottom face of the cube, which is also moving. You could probably lose that by making the cube very tall and putting the ocean floor above the lower movement, or at the risk of slowing things down unbearably, you could chop it off with a boole.
The problem still remains as to how you would transition from a wide open ocean shot to this, but at least it is a viable solution for seeing above and below water, and should allow you to have light beams in the water below that are actually related to the movement of the ocean surface.