On a song like cottontail, I still can’t play it perfectly at speed, so I’ll stick to what’s written until I can.

I fudge together a metronomic base line in the left hand and voice all chords with the right hand so the melody note is at the top (I don’t play the root in the right hand unless it’s the melody note).

Once I can do that easily without any halting or mistakes, I’ll start to improvise.

Wouldn’t dare to play with “real” players as I often haven’t heard the recording and am blissfully unaware of the missing comping, licks, etc. Most of the time when I finally listen to the recording of a song I love, I don’t even like it. No one plays the melody and everyone’s showing off. It’s fun to experience live, but often sounds too busy and aggressive as a recording.

I guess that’s a matter of taste. I enjoy sparse music unless it’s rigorously orchestrated (eg I love listening to Cuban music, which is quite busy, but everything fits together perfectly)