Chuck,
you wrote "I have in the range of 4000 - 5000 pieces of music in my music library. There is no way an ear player can memorize that many tunes."

There are exceptions. I had a friend (back in the 60's) that played organ in a restaurant bar on weekends. He would routinely play six hours straight without music and could play properly almost anything that anyone requested. (He also would go the six hours with only one break).
He had memory and kidneys to match!
I tested him quite a few times by asking for oddball, old , or brand new songs and he always came through. I believe that he only had to hear the song once and he had it nailed. Not only the verse, but the breaks, the repeats - the whole thing.
Truly amazing.
Walt