Why didn't I think of that before

Here's a new build, it saves to egc-sdl-test.log in your SD card:
https://github.com/embedded-game-controller/egc-sdl-test/releases/tag/0.3-wiiu4
Everytime you restart the app, the log file is created anew -- previous contents are lost.
Please press only one button at once, and write down the order in which you press the buttons, so that I can correlate with the logs. AFAIU, this controller should also have an accelerometer and a gyroscope: did you see a set of bytes continuosly changing there values, while moving the controller? If not, there's probably some more commands we need to send to it in order to enable them.