Man, I thought that was lovely. Good tone, flow and feeling. I listen less to the engineering side as that's just a matter of knobs and buttons that anyone without talent can lean to do. If commenting about the mix I thought that possibly the sax was too far forward as you could hear the keys clatter and attacks sounded harder than they actually were. Anyway, that's not important.
I don't know where the backing comes from but it's a nice balanced approach. The trick bit with this backing is that it goes from backing to playing the melody at times. Where that happens it's more important if also playing the melody to mesh. Not quite clean if they or you have different entrance for the melodic line (on beat vs. dramatic pause after-beat). Whenever this happened I just wished that the piano wasn't playing as your interpretation was good. Maybe use a different backing that doesn't play the melody? Alternatively give the melody over occasionally and play harmony/backing?
No matter. Very fine playing that sounded natural and heart-felt.