ProtoDome, Nase and ShadowBlade:
Thank you so much for your very helpful feedback!
To eliminate the possibility that some/all of the audio problems in the video are related to the YouTube conversion, I decided to upload an mp3 instead:
https://sites.google.com/site/pianodemos/files/moon_theme.mp3
The problem with hissing and distortion is one that frustrates me. The piano I used for this recording was PianoTeq, which is based on physical modelling rather than sampling. If you do not tweak it exactly right, it seems to cause a lot of weird audio effects, at least in some speakers/headphones.
Anyway. I also turned on PianoTeq's internal limiter and normalized the clip.
So; did any issues get resolved? If not, do you have any specific recommendations on what could be done eq- or compressor-wise?
Again, thank you so much!