I ran into some of the bugs already mentioned here with my network configuration (unable to delete, ghost controllers, etc) and would like to completely reset my network configuration, ideally making it so the files on disk/info in the world save are exactly how they were before I started messing with the mod. Is the network data stored in some TileEntity or something in the world save data or is it in a separate file somewhere else?

It's stored in the world nbt data. Which you can find in "Server Path"/world/data. the file is called "sonar.flux.networks.configurations"