Thanks for the input so far, guys!  I've already tried turning the Cornea invisible and just using the EyeReflection zone.  Still got the ring.  It's weird, because the makeshift cornea/eye-surface combos that I made out of sphere primitives for Genesis 1 worked just fine, and they presumably hugged the eyeballs just as closely.

For the moment, I'll see if I can tinker with the bias again.  Higher or lower?