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In fairness to one of my teachers, he did not say a Major 6 chord without a 9 sounded "White" ... as I remember now, he said "Vanilla."
Since you end your composition with the voicing A E A C# F# I would probably change it to A E B C# F# for a little more color since it's the final statement.
I also like how you play that A major 7th chord (A, C#, E, G# ) and you start it with the A harmonic ... very nice.
I'm not wild about modulating to parallel Minor Keys... (A Major to A Minor in this case) unless the modulation has a more modal shift
where you can borrow from several different Tonal Centers ... but since your playing is strong and assertive there it works well... I would
have probably modulated to F# minor myself and written/composed there for a little while.
I also like the way you pick up that D Major 7 chord... (D, F#, A, C# ) ... it's is a nice motif development from that A major 7 and it's
diatonic to your key. I would probably pick up the root D as a harmonic too so that it ties together with that A Major 7th with the harmonic
Compose, Compose, Compose,