Um....

Im telling you.... just move the skybox out far away from your map, and the problem will go away. If there is one part of your map that has high walls, put it on the other side of that area. What you're seeing sounds pretty normal, and begs the questoin: "if I had to write a sky-projector, then how would I get it to ignore the main level? You can't and still get the desired affect. Decompile de_dust/dust2, or spectate any of the valve maps, and you will see that they've designed around this problem by placing the skybox where 100% of it is occluded from the player's view, even if that occlusion occurs only because of distance.