By Heart and by Ear

I'm still digesting the experience I had of playing a 3 night gig last week.  A friend of ours took this video of us playing "Softly as a Morning Sunrise," and I'm pretty satisfied with the way it sounds (not with the quality of the recording).
That's a song that I know by heart, backward and forward, and you may notice that the music stand in front of me is empty.  When I soloed, I knew just where I was in the song, and I could hear the relationship between what I was playing and the tune and the chords.  But most of the time, even though I know a song pretty well, I'm afraid to play it without the notes in front of me, and I know that's a deficit in my playing.  It means I'm using my eyes to keep my place in the song instead of using my ears.
By now I know a lot of songs by heart, and the expression is extremely apt.  My unwillingness to trust my heart, as it were, and play the songs without the written music in front of my eyes, is holding me back musically.  My dependence on my eyes cuts my ears off from my heart, and my playing is intellectual rather than emotional and natural.
What's strange to me is that when I play a song that I do know well by heart, like "Embraceable You" or "It's Only a Paper Moon," if I've started to play the song from the written notes, I find it almost impossible to tear my eyes away from the music and launch myself into playing it by ear.  I have to learn to trust my heart and my ears.