I think it would be foolish of me to tell you how to execute an autorotation using the A team theme.
The point is that you need to lighten up a bit...or at least i needed to lighten up when I was in the same situation. Using something like humming a tune is mearly a way to lighten up and take a bit of the over-seriousness that you have created away. We all know that when you tense up, your control inputs become less smooth, and sometimes mechanical. It is this that I believe was creating my bad autos. Simply by making myself relax a little, everything just came together.
At the end of the day, you probably know how to do everything you need to demonstrate in your flight test. You probably know how to do most, or all of it well. The only difference is that there will be more pressure during the flight test, and you are the one creating that pressure, so find something that will make you chill out a bit...preferably not drugs or alcohol!