I just finished your game and I am dying laughing. That was hilarious!
This brought me back to the flash animation day where games on NewGrounds were coming out daily. They were short and wacky!
Since this is more of a tongue in cheek game, I don't think you need to improve his singing since...well...he just isn't good. But, we could improve just the tones that are played with the key presses on two fronts
Take a song and hum or gibberish sing it. Try to make the important notes more obvious in your voice. You will use those when you are deciding what "notes" to put on screen.
Then instead of arrow keys equal a certain tone, they are just used to make sure he is still singing along with the song instead. If he gets off time or misses a note, then you play the god awful tones from this game.
I love this game so much. I had a good laugh playing this game! Great job!