Found the culprit. I was right, there is a HUGE amount of space between the heatsink cold plate and the die. Like see right through to the other side huge.

Which plate?

 


Part circled in red is the gap between the heatsink and the die.

Everything seems to be sitting fine.

Doesn't make a difference in the space between the cold plate and the die.

Don't have an actual camera available with me but I can tell you that the gap between the die and the cold plate is about 1mm which seems a bit too big to be just an alignment issue, especially since all the screw holes match up.
 
I'm really hesitant to try much more because of how many times I've screwed and unscrewed screws and slotted and removed the graphics card, I'm fairly afraid of wear and tear on the card.

i can see that the thermal pad nearest the output ports isn't in the same place between your photo's.

Well, I moved it and it makes absolutely no difference whatsoever. I'm not sure if I can emphasize just how big a space there is between the cold plate and the die. There's no pad on either the pcb or the heatsink that can make a space that big and not have any sort of give at all.
 
If I were to look through the space, I can actually READ this forum through it, that's how big it is.
 
The first time I removed the heatsink from my 660, there was a lot more TIM than what yours is showing, if I remember right.

I'm just going to wait and see if EVGA will approve an RMA at this point. If not, I'll get back to trying to figure out what's wrong with this.