Even with a correct mapping you can't avoid the skewing at the top, because it comes from the texture used. You are doing a cylindrical projection mapping, but this texture isn't suited for that, you need a specifically tailored texture for that. Skydomes are annoying to create because of that... (for instance
here is the texture I used as a base for the Ahra Pahts sky, notice the distortion at the top?).
Heck if you look at the skydome in Ae'gura you can notice a severe pinching in the middle; probably much like the one you have on your sky.
And yet they should.

Haha; took me a couple second to get it

. (shame on me, I'm a road runner fan)