Jack,

I may need to go back and have another look, but I understand Summertime to be functional, with the tonic chord alternating between Am/maj6 and Am/maj7.

As you correctly point out, the melody omits the Maj6 and the Maj7, but the final cadence is a very functional one being constructed of a 4 chord turnaround into the tonic using chords I maj7 - IV maj7 in the Key of C (Cmaj7 and Fmaj7) followed by chords II half-dim - V7flat9 - Im/maj6 in the key of A minor (B half-diminished - E7flat9 - Am/maj6).

What makes this particularly sweet is that Fmaj7 and Bhalf-dim are the same chord with a different root - so omit the F in Fmaj7 and put a B n its place whilst keeping all the other notes the same and you get Bhalf-dim.

Te result, a seamless modulation from Cmajor to its relative minor.