(Regarding title of Shemp solo Columbia shorts titles music):
...I figured he might, especially since he listed the arrangers of this particular version of the song. And I have no doubt his records say "Merrily we Roll Along", and I have no doubt whatsoever that I'm wrong.........
No, I wouldn't say you're wrong!
As you have pointed out, that tune could match several other sets of words from other songs.
Yes, I was referring to offficial studio records that identify the tune as "Merrily We Roll Along". The documents I've been using are just about as "official" as you can get: the Music Cue Sheets that Columbia was required to submit to the music publishers (ASCAP, etc.) to ensure that the composers and publishers were properly credited (very important to be documented for reimbursement when the music is used for any public performance). The cue sheets list info such as the composition's title, composer/arranger, publisher, extent of use in the film (entire or partial), whether performed visually, vocal, instrumental, etc., timings, etc.
Sometimes cue sheets reveal if a selection was taken from an earlier film, whether a selection may have been used from a record, and other fascinating facts.
Among the many thousands of cue sheets (for every studio, not just Columbia) that I have, there are hundreds from Columbia shorts including the non-Stooges Columbias that use the opening titles music you asked about. They all identify the tune as "Merrily We Roll Along" with Leigh Harline and Ben Oakland as arrangers. In the late 1940's Lyle "Spud" Murphy took over as arranger but the title of the tune stayed the same.
The info on cue sheets is not always perfect. I have found many errors, omissions, etc. over the years. I'm just reporting here what Columbia submitted as the official composer/arranger credit for the tune.
By the way, to make things even more confusing, I do have a cue sheet for one 1940's Columbia short for which the titles music is given as "Good Night Ladies" but that's crossed out and "Merrily We Roll Along" is written in.