I'm not sure why I didn't think of this earlier but I messed around with adding an alpha to the mix.

- node setup in cycles for Lilibeth's green eyes
This produced much better results as here:

- Rendered Lilibeth with alpha mask
There are still strange artifacts that I have not been able to figure out how to get rid of, or where they are coming from.
Peter L. Berghold <peter@berghold.net> or <Salty.Cowdawg@gmail.com>
Retired IT with 30+ years in the business