Very good points, Nilzner
I agree with you. I always think that having a detailed chart and accurate transcription of a recording is the best way to learn a song. Nothing can replace listening to the song to get all the details a chart can't provide. But starting with a detailed chart is a good start. Once the song is properly learnt, the chart is not even needed anymore, or it can be simplified to give more freedom for interpretation.
I also figured that some parts had to be simplified in order to fit everything in a single page.
I agree with the Eb-Maj7 chord. I can hear it in the recording. The choice to use an Eb-6 instead is simply because the voicing/inversion of the Eb-Maj7 generated by the iReal pro player didn't really sound right to my ears. Also, like you said, it's mainly played by the keyboard. However, I'll listen to it again.
Yes, Ab13/Eb is very similar to Eb-69. I probably used that chord because I've heard an Ab played by the piano on top of it. However, it can go both way I think. To be consistent, it's probably better to write a Eb-6 or Eb-69
About the E9#5, it's possible that a #5 is played by either the guitar or piano at some point (I will have another listen), but I still think the #11 or b5 is the main alteration. It sounds more accurate to me when played with the melody.
However, this is very subjective. By experience, I've learned that it's not because a note is heard in a chord that the actual chord has to include that note.
It often happen with 7th chord (as a tonic chord, not dominant). Even we can actually hear the b7, the chord is basically a major triad, not a 7th chord. This happens a lot in blues related songs.
About the Ab13 at the end of the whistling section, you're probably right. I've also noticed that the #11 is not always played on that chord. I've probably added it for consistency with other similar sections. However, it doesn't sound wrong because the #11 is implied anyway. But I will give another listen again more carefully to see which one sounds best.