Hopefully it will help others to know that with patience, which I had run out of, it is possible to get this job done. I'm going to try to adopt that attitude with the rest of my networking project. I think that now that I know the hardware (X-Surf 3) actually works and that my future problems (for I do expect some) will be of a software nature, I can bring more patience to the table. Thanks for the encouragement.
I take it that EasyNet and Genesis both are "front ends" for setting up an AmiTCP stack, so if that's the case maybe I don't have much in the way of "extra" files floating around. I deleted the Genesis directory and got rid of a an extra AmiTCP assign for Gensis, and my EasyNet setup still finds the Internet as it should. So, now I'm connected to the whole world. Next, I need to get connected to the other computers in the more immediate vicinity (my house!).
I have to decide whether to register IBrowse or just use AWeb. I really only need Internet access on the Miggy to grab files on Aminet and the like, as I certainly have a wealth of "modern browsers" on other machines. Still, I want to encourage commercial Amiga software development wherever it still exists, so I may register anyway.