In the meantime I was testing a few things. I rendered another version, but it wasn't worth of sharing here, since it wasn't very different to the previous one.
More or less accidentally I found an interesting way for the white water. I was trying some blue nodes (ME!!!! BLUE NODES!!!!!) and found the "get normal" node. Plugged into the Breakup slot I got a multicolor weird LSD like coloration, but when I did a test animtion I found, that some of the colors behave the way I wanted them to. So I used some other nodes, i. e. the blue to scalar and the green to scalar nodes and played with some color adjust shaders and fed the breakup slot and the mask slot of a white shader with it. I had to adjust the settings for a while, but in the end I liked the result.
For testing purposes I switched off the cloud shader that represents the mist and cropped the render. I only rendered frames 100 to 425, because this is the time where the most is happening.
Still some work to do, and it's far away from perfect, but given the fact, that TG has no fluid simulation, I'm quite happy with it so far.