It's a good question, and one i'd pondered several times wrt The live album versus the single.
Soul Inc members had come via iterations of the Medallions, Pieces of Eight, etc. to form as Soul Inc in about Sept 1966. "Good To The Last Drop/What Goes Up Must Come Down" was being touted as a release in Autum 1967 and a major West Coast label were interested in the band.
The Cellar in Charlotte, NC (where the Emblem label had the live performance recorded) opened in April 1965. Artists that played there included The Tams, Major Lance, and Barbara Lewis to name a few.
In April 1968 Soul Inc at The Cellar ( this relates to the LP) was also being touted as released.
So, on Discographies we have,
Soul Inc, S-100 / S-101, as 1967. Recorded Live at The Cellar
Soul Inc, LP 106 live at The Cellar, as 1968
The Charms, E109, as 1969
I think it's safe to assume that Soul Inc, were only live at The Cellar once where a recording was made. I doubt anyone would set up a mobile recording facility for a single (S-100) and then again for a LP (106) sometime later. In which case the Single & LP release dates may be wrong. Could the Single have been released from the LP? But how, it can't have been released in 1967 if the Live recorded album hadn't been recorded until 1968?
It's not to say he (Joe) didn't have one, but I don't know of any mobile recording facility at Joe Huffman's Mark V studio in Greenville. So i suspect S 100 was likely something that he produced but wasn't recording at his Studio.