C6 chord over D and 3 C notes in right hand, then Am7. The chords contain the same notes. The proximity to the right hand doesn't allow for rearrangement of chord notes. Why does the author not just repeat C6? How is this intended to be played? What is the best transition?
That's just for root movement. So, measures 7 ad 8 are:
C6 Am7 Dm7 G7
Am7 leads to the
Dm7 much more naturally that
C6 -> Dm7 would.
Also, right before the
C6 in measure 7 is a
G7 so that resolving to
C6 instead of
Am7 makes a lot of sense as well.
Remember, the strongest root movement in western music is
V -> I. A good first place to start when figuring out why a certain progression is the way it is, is to look at root movements between chords.