When I began listening t jazz in 1961 I to discover that Topsy was originally by the Basie band.  I just checked it on  Spotify and saw that it haas twice as many plays (6 million) as One O'clock Jump. 

Time for some Pops. Never can have enough. This is prime Louis. Louis Armstrong “The Alternate Takes In Chronological Order Volume 2 1935-1944” Neatwork cd   300×300 11.5 KB

Re-visiting this recent Resonance Records 2 cd reissue of Rahsaan Roland Kirk “Seek & Listen: Live at the Penthouse.” I’m listening to disc 1 Was there anyone else really like Kirk? He was unique in several ways. And I think one of the few who really deserve to be called a genius.  

Thanks!

OTOH, "Honky Tonk" figured as such (either without singling out one part or by naming both parts simultaneously) in the chart listings wherever you looked. (Billboard, Cash Box etc.) So apparently the tune was treated as one entity.  Two random examples: The below excerpts from Billboard of 22 September 1956 and Cash Box of 1 Sept. 1956. Whereas it was "Topsy Part 2" that was the hit. I don't know if Part 2 was pushed intentionally, but maybe the more organ-heavy Part 2 was considered to have more hit potential in 1958 than the horn-led Part 1.  Your explanation about who would have been more inspired by whom in exploring Part 1 or 2 of "Honky Tonk", wearing out the respective sides, does sound plausible, anyway. I wonder, though, if Phil Schaap's observation was anecdotical or if he actually had had several dozen copies of the originals in his hands.