...with Mike that Benny's recall of the date of "Clarinetitis" as being Feb 1927 is right. I have gone over Connor's resumé of this subject several times in "BG: on the Record", although I confess I have some trouble connecting the dots of his reasoning in places.
(...and Mike, I had assembled an almost identical post to yours! So there's not much to add!)
I think what is key to the argument is: Connor says the Chicago mx are "false matrices" as they "jibe" (agree) with the true matrices for the Pettis date. I'm not sure what this means exactly. The "E" matrices were assigned by Vocalion to NYC sessions, and "That's aplenty" and "Clarinetitis" were cut in Chicago and so their mx's are wrong. It seems strange that the numerical numbering of the Pettis sides and BG trio sides is consecutive. This doesn't make too much sense being two cities apart! It does sound like Vocalion's record keeping is skewed?
Also, perhaps most important, in February 1927, the Pollack band was was booked in the Southmoor Hotel, Chicago!
E 7397 BG trio rec Chicago, Feb 1927
E 7398
E 7398E 7394 Pettis rec NYC June 20, 1928
E 7395
E 7396
For Albert's chronology:
In early spring 1927, Benny did the "100 Jazz Breaks" on dictaphone for Melrose in Chicago. (Connor)
