I really wanted the standard ADTPro Ethernet connection to work properly so that I don't have to start the ADTPro Server from the command line. Unfortunately, that connection type adds a byte to the start of the ADT packet indicating the packet number. That seems appropriate for the UDP protocol that is used, but that one byte confuses the Apple II client enough that it immediately reports an error. Commenting-out the code that adds the packet number byte allowed me to get everything working, at the expense of out-of-order packets not getting re-ordered. Not a great solution, but it is more convenient now. Really, ADTPro Server just needs a decent interface for its SerialIP mode.
Full details on the ADTPro Support Forum.
I really like this USR-WIFI232 compared to an Apple II ethernet card. It is compatible with anything that uses the Apple SSC card, has a nice web interface for configuring it, and includes WiFi, at a little over 1/2 the price. Unfortunately, the user guide can be a bit hard to decipher.