They may have been "town"teams or club teams...I know some towns had Knights of Pythias that would field a football team and play others and even High School teams. The "Outsiders" that sounds like a town/club team to me
My money is...Ad Hall and Sharp were HS team and the other 2 were club teams of some kind...I could be wrong about Seaton but that mascot is kind of like the ones I have see for town or club teams during that era...I think Merkel had one in the mid 30s...maybe Rising Star as well...
There were a few colleges that played six-man on some level...I have seen a few and have photos of some (all over the country)...I am not well versed enough on how they were made up or the purpose for them fielding a six-man team...the ones that did had both a six-man and an 11-man team in almost all cases...OBK might be able to shed light on it more...
In WWII six-man football was used as a rec. sport by the military...maybe in some camps and bases up into the 50s...once on ebay there was a team photo of one of the league champions from a WWII base...I didn't win the bid...
CT6MFL: these sources may help you if you wanted to find out about those schools
Lelia M. Batte, History of Milam County, Texas (San Antonio: Naylor, 1956). Milam County Heritage Preservation Society, Matchless Milam: History of Milam County (Dallas: Taylor, 1984).
Speaking of box scores, Temples paper had a big list going in 1938 and on. If anyone needes them let me know.
From what I gathers TJC played the game against San Gabriel as a road show to help fund a regular football program. I never even knew they ever had a football program till yesterday.