That's a great idea, hborre.  I did more research about eye anatomy; that thing that takes up most of the lacrimal zone on Daz figures is called the caruncula, and it is basically skin over a mass of sebaceous glands and sweat glands (eye sweat, YUM).  So I hue-filled the lacrimal to match the skin and then used a blender node to mix it with a Simple Color of the blood color. I like this much better!

I'm going to take a break and get some sleep, thanks for the help. Still a long way to go before I am satisfied, but I have made a decent enough amount of progress to call it a night.