The 0,0,0 thing is misdirection. People say to center your map on that so making the 3D skybox is easier, but in reality there's no reason that's much easier than anything else.
Here's what you do:
Put a sky_camera at a point in your map. Then copy important geometry (buildings, ground) and the camera and place it in a separate skybox area. This is your 3D skybox. Delete the camera in your main level.
With your 3D sky selected, hit Ctrl M and reduce everything in size by .0625. Create extra 3D sky around your important geometry from earlier and then delete it. This way your 3D skybox doesn't include anything from your old map anymore.
As long as you don't move your sky_camera around and it's still oriented correctly in your 3D skybox as it was in your level, everything will line up right.
Does that make sense?
Also, yes, you want to have some terrain players can't get to in your map before the 3D skybox starts. Load up a
decompiled Valve map (a small one so it's easier) and look at what they are doing with regards to that. Fly outside their level and look around: you should find a separate skybox area that's much smaller. That's the 3D skybox. Hopefully by doing this you can understand what we mean. It's kinda tricky.