A point to bear in mind - and I had exactly this trouble when I first
started using lilypond ...
\transpose changes the pitch of the notes as internally represented
within lilypond. As such, I tend to think of it as a device for
inputting from and outputting to paper.
\transposition (as far as I can make out) is a midi construct, that
alters the pitch of sound output.
Even as I write this, it doesn't quite make sense to me, but bearing in
mind I do not use midi at all, and I originally tried to use
\transposition and was told to use \transpose instead ...