Just making a note here because google failed to find anything when I was trying to solve this problem:
I added the env_fog_controller entities, but I was mostly concerned with the effect on the middle area which doesn't really need a 3D skybox, so I didn't make one. When I compiled and went in-game, it behaved as if I had a relatively short Z clip plane of somewhere between 3000 and 5000 units. It was completely failing to render any visleaves beyond those measurements, resulting in some awful gaping holes on the far side of the lake, some of which would pop into existence as you walked farther towards the middle.
I tried setting the Z clip plane higher, and tried setting it to -1 (don't clip), and tried adjusting the fog end parameter, and nothing had any effect on the problem.
The solution, as it turns out, was to create a 3D skybox. Even with nothing in it but the sky_camera, suddenly my Z clip plane settings started working, and everything looked fine.
So hopefully this will benefit the next person who runs into this problem and turns to google for help.