I'm having an incredibly similar issue that I think is worth pointing out. To shed a little more light onto this, it's that you can't use the Gecko OS if you're using a Wii Remote that has Wii motion plus built in. I figured this out a while back when trying to play Project M with a friend. They only had 1 Wii Remote with Wiimotion plus built in, and I didn't know why their Wiiremote blacked out then. When I got my own Wii remote with Wiimotion plus built in ((just to test this I used two Wiimotion plus built in remotes since my friend had one)) and it's just that the Gecko OS can't handle it for some reason.
If you use a regular Wii remote and have a Wii motion+ attachment, it works fine. If you use one with Wii Motion+ Built in, it won't work and you can't start up Project M.
Also I should point out that this isn't a Wii U thing. The same thing is true even if you start it up on a regular Nintendo Wii.