This was a completely blind speedrun, so please excuse the copious mistakes, there's plenty of room to optimize. I had a feeling that this would be possible, and was able to confirm it once I found out that your gold moves would get saved after you quit.

The current route is based on doing as little of each song as possible, while maximizing the number of gold moves you can get during each song. We try to leave the beginner routine as soon as we get the required 3 or so gold moves to unlock the next routine, where we have access to more moves.