It sounds like you are on the right track in what you are doing. The ways I know how to transpose the pitch of an audio file are the following:
1.
Process->Transpose. I haven't used this much so I don't know how far you can go without it sounding funny
2. Use a program like Melodyne that analyses the audio and lets you move the pitches around.
As far as I know commands like "groove clips", "Fit to Time", "Length" etc don't change the pitch of clips only their timing.
If you are transposing many tracks and they are not staying in sync then one thing you can do is mix all the tracks together and export them as one stereo full song. Then you can transpose the whole song. Of course this would also transpose drums and everything with it. If you don't want the drums or other non-pitched instruments to change then you will have to transpose tracks individually and then play them together to make sure that they are in sync. If they aren't then you may have to do
Process->Fit to Time to make them slightly longer or shorter to match up in time.
Sounds like you have tried some of these so good luck