OK, thanks Rylius, now I can see the skybox at certain angles/distances, but at other angles/distances I can see right through it onto the ceiling (which is orange-ish; compared to blue sky):
(here's the sky)
(hare's the ceiling (which is above the skybox))
.
I will make a work-around for this issue by making a hole in the ceiling and placing the skybox there to fill in the hole, but it feels kinda stupid*.
*It will look more like my original idea, but it makes me less lazy to do it.