I made a PR to add Wii/Wii Mini support: https://github.com/doworian/vWii-Ethernet-Patcher/pull/2
Edit: While I was able to make the network work with my changes on a Wii Mini, it threw me down a rabbit hole where several mishaps on my own made...
Hope you keep having some progress with the project and fun with it. It would be very big with a fix for Wii since it can be hard to come by more AX88772 adapters now. I have tried to buy one multiple times in Norway now and keep getting wrong...