I think I have solved the problem. While running Mac OS 8.1, the Ethernet still failed when trying to switch the AppleTalk control panel. I downloaded both versions of the Sonic Systems NIC drivers from
http://www.macdrivermuseum.net/network.shtml. I initially tried version 6.1, since the 7.8 version only stated an update for PCI cards. The Ethernet card failed with 6.1. On a whim, I decided to try version 7.8.
After 7.8 was installed, my Ethernet selection changed from Ethernet to Ethernet Slot 1 and Alternate Ethernet. Slot 1 failed, but Alternate Ethernet worked like a charm! I was able to see my HP LaserJet 6MP on the network as well as file share with my PowerBook G4 booted into OS 9. Due to changes to networking in Mac OS X, I cannot see the LC 575 with my iMac, and the LC 575 cannot see my iMac.
Now I am going to swap hard drives and see if the 7.8 Ethernet software works under System 7.1.