In the top-10 from my "desert-island discs" collection.
Even if Tatum piano lines as accompanist are sometimes "too intrusive", I also have this boxed set in high regard. Norman Granz's mission of extensively documenting Tatum in the "Solo" and "Group Masterpieces" sets is much appreciated.
And +1 for the Tatum-Webster disc as a favourite.
Currently listening to
Your recommendation of the Savoy 2-LP set is seconded. (Must be "The Most Versatile Band in the Land" - Savoy SJL 2261 with tracks from the Hit and Majestic labels that were bought up by Savoy). 17 or the 24 tracks are arranged by Sauter.
But to those triggered by the music examples in your post: the three Youtube tracks you have linked to are not on that set. All three originally were recorded for RCA and were on a 1955 RCA Camden LP, according to the discographies. "Cyclops" and "Idiot's Delight" also are on "Howdy Friends" (Limited Edition LP 102).