One very strange thing..
I opened the eye OBJ in Lightwave and the center point of the pupil is actually 32 vertices stacked on top of each other, resulting in 32 non planar polygons that are actually quads, that anyone would guess are triangles just by looking. Strangely enough, they act like welded points, but aren't. That is, you can grab one of those polys and move it and all the rest go along for the ride. if those points weren't welded, it would come apart at the center. I have to say I've never seen that kind of behavior before.
Not that that doesn't work, but it could create render artifacts in some programs. I'll do some render tests and see what happens. Putting it into SubD typically solves any such issues, but you never know til you actually try it.
The UVs are distorted really badly towards the outer edges,which is what will happen when you planar map a half sphere straight down the Z axis.