It is Ben Webster on track 14.
You have found the correct CD for this version of "The Peacocks."
Track 2 is going to surprise some folks.
Track 3 is Paul Gonsalves. Now what is the composition?
Track 4 is Eric Dolphy on clarinet.
Track 7 is correctly identified by title.
Track 11 is correct, I had no idea it had been used previously. I went to the link you provided then clicked on the allmusic.com link and was surprised to find my review of this CD attached to a different CD by Toshiko Akiyoshi with a similar title. During my 14 years of writing for them, I found that the data entry folks frequently had no idea what they were doing, while the editors would randomly change star ratings, so a glowing review might end up with 3 stars.
Track 13 is Just Friends.
Track 14 is Ben Webster, but Art Tatum is not the pianist, this track was recorded after Tatum's death.
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Keep those guesses and comments coming, everyone!