If you want to deal with the ringing, try using an equalizer to lower the volume of that frequency. It's takes a lot of practice, and I'm quite bad at it myself, but learning to EQ can really help you sculpt sounds the way you want.
If you want to go even further in realism, play with tempo changes. Slow down slightly toward the end of phrases. Try decaying the volume toward the end of sustained notes. I think you did that around :30 and it sounded nice.
Nice job! :)