The original poster mentioned the C & C# notes not being 'on pitch' with the supplied recommended fingerings. On some instruments I have, the 'standard fingerings' have to be varied somewhat by changing which fingerholes are open or closed for these notes. However, when playing very fast, some of these instruments produce notes which, while 'off' are not noticed to be objectionable.

Also if one if not playing 'Classical Symphonic Orchestral Ensemble' style music, but 'Folk Music', some of the notes being slightly 'off' is accepted as part of the 'character' of the music.

Robin