Hmmm. Maybe I am missing something.
Let me get this straight. You edited in audio units and verified that the clips started at the beginning of a frame. Then when you moved the clips, they slipped in time? To where? If they started at the beginning of a frame, where are they after you move them?
I understand the problem if you don't start at the beginning of a frame, but not if you do.
Perhaps you can take a bunch of screen shots and show us exactly what is happening?