For one, your chords are not quite right. Understanding the chords in context will make the song a lot easier to understand.
Here are the right chords:
A7 --- / Cm6 --- / G/B --- / Bbdim --- / Am7 --- / D7 --- / G6 --- / ---- /
Think about it like this
II7 --- / iv --- / I --- / iiibdim --- / ii7 --- / V7 ---- / I --- / ---- /
Some things to think about in any pre-bop style. These are some the essential harmonic hallmarks of the dixie / hot jazz / swing / hot club styles.
Generally, all minor chords are voiced as min6 chords, unless they are part of a ii-V move, in which case it'd be a min7. Most major chords are voiced as 6th - never as a maj7, unless its a II7 or V7.