@DJTHED  
I do like the shine of the eyes on this render, and yeah, I think the sharpness helps. The only concern I have with the test render you made is that it looks like the cornea changes the shape of the eye at the boundary of the iris and pupil - it actually covers the iris as well.
 
Something interesting you could try rigging is to have the area covered by the pupil actually getting more and less reflective as the aperture of the eye changes. I’m not sure it’d be “realistic,” but it might help with certain expressions. For instance, it’d up the contrast on gasps like this…  
 
while allowing for big, glossy eyes on exaggerated stuff like this.  

@WingbeatPony  
Quick question. Do you prefer the shiny reflectivity of the eyes here, or the reflectivity in this:
 
Also tried making the depth of the pupil less prominent as you recommended to make it look less like there were more than one light source shining on the eye from that angle.  

 
I also tried increasing the sharpness of the reflection based on what you mentioned about cataract, and how it didn’t look as sharp as the textured eye shines. What do you think?

The natural reflections look okay on the sclera of the eye, (and would probably look ok over the iris as well), but the one in the pupil clashes imo. With the crisp, white false highlights, the real one just looks like a cataract. I’m sure you could change it up at one edge or the other of the iris, see how it looks.
 
Edit: what also makes this look funky is that it looks like the square light source reflected in the eye is being reflected in two different places, which might be accurate on an eye with a real lens but it’s pretty clear you’re going for some hybrid between realistic lighting and ‘toony materials. My approach in a situation like that would be to let the iris have some depth in the texture, but leave the specular highlights behaving as though they’re on a single convex shape.