Really play down the diddles on the snare drum. They're almost ghost notes on the recording.
One caveat is that, while it's very good, standard notation can't capture every nuance of a musical idea or phrase. Like many others, I believe that the real music happens beyond the black and white of the printed music. So listen carefully, practice the printed transcription, and then experiment with your interpretation. And if you find a better way to write it, let me know!