I finally have gotten Rhyse's mod to load, only to run into a new problem. Despite all efforts to direct the download into my Firaxis directory, I finally noticed that there was, from a previous download, a set of files in my Infogames directory that had a larger Pedialcons file. So I copied the files in that directory into the Firaxis directory, which resulted in at least bringing up the initial screen.
However, I am now getting an arts/units/ancient_settler.... file not found error message, which kicks me out of the program. I notice this is a message listed on the FAQ page. One of the suggestions is "Check that your ...\Civilization III\art\units folder contains this." "This" seems to be a link that is no longer working, at least for me.