Thank you for the help!
First of all: The scalar worked! All I needed to do was changing the viewing scale.
I used the v2 cloud, because that was what the tutorial used.
And, yes, at least part of my problems may be because the textures don't move with the cloud. Thank you for the information!
I tried an alternative route, by using an image as a mask instead of the node network. That did not work either. No matter what I tried, the mask did not actually mask anything. That may well have to do with the mask being in the wrong place. I did set it to use the same coordinates as the cloud itself though.
The only thing I managed to do that affected the size of the cloud, was directly changing the size parameters, but then I ended up with a not-the-leat-bit waterfally floating ball of fog.
Right now, I am torn between either using the entire setup from the tutorial file, and build the environment around the waterfall, or, to rebuild everything from scratch using the v3 cloud instead.
I think I'll try the v3 variant first. Might be a little bit easier.
It is worth the effort to experiment a bit. A nice looking, parameterized, reusable waterfall, would be a useful thing to have.