Shifting isn't really possible because of the distortion of the cube maps. The easy start has at least two pirate bases, so you would need to adjust those spots too.
It's probably easier to begin a new Easy Start in creative mode and cut/paste the buildings to new locations.

Would it be practical to shift around the height map until the ground under the "Easy Start Alien" would be at the right height? I know it's a cube map, but do not know what it entails to shift it horizontally. It's a bummer that this is both so beautiful, but then incompatible with a standard start option. =/

It works with No so smooth voxels.
If you add it to an existing save then the already existing grids might be below or above ground. Also, any changed voxels from mining or collision will stay. They can be reset globally with the admin menu.
Other than that there should be no issue. Better make a backup before.

Superb.
Does it work with Not so smooth voxels? I assume not. And, for the visited alien planet part, to add it it into an existing save, if this because of structures/boulders? Let's say they ( and the .... entries) would get cleaned via admin, and no grid exists there, would it be save to add it middgame?

Excellent work. I never realized Earth and Alien maps are the same.