Did we ever decide who officially composed this song? If not, I believe I may have a solution.

In regards to the multiple copyrights belonging to Wally Fowler, and Ray Stevens (et al), I believe the assumption that would make sense is that the song is a "traditional" song in the public domain, and Wally and Ray's versions have some unique aspect that allowed them to put their own copyright on it.

If that's the case (it being a traditional tune, that is), that would explain the multiple copyright claims on one song and why it seems to be so hard to nail it down (as I've found claims for R A Searles & Asa Hull and Lewis Hartsough and the other ones found above)