How Do I Fix Bulging Eyes During Animation?

I have been modding a character mesh from a game (Mass Effect 3) and have it about 99% finished. I've given the character a new face and weighted it so it works in game as expected EXCEPT the eyes. The eyes look fine in 3ds Max but as soon as I apply an animation to it in 3ds OR import it into the game and have the game animate it, the eyes shift upwards and bulge outwards a bit.

Here's an image of her in 3ds frozen in mid-animation. You can see the eyes bulging out above her eyelids.

How do I correct this? As soon as I enter "Editable Mesh" mod everything pops down into proper place.