Is it possible to do as the title suggests? It currently looks like this:
What both Valve and I do is to make a 1 unit brush at the edges of the water with the toolsblack texture, then make it some units short of touching the surface, so you don’t see a black edge from outside. However this means that a little part will be not covered.
Ideally if you have skills to 2D art is to use some sort of colored texture so it blends with the water ( with maybe some sort of secondary texture with distortions via Proxies ).
I was playing around with water_lod_control and I noticed that setting both values in it to 0 makes a black wall that covers the entire edges of the water and is invisible from top of water. Looks pretty good.