Interestingly, you will search in vain for Florida State on the 1938 map as they were the "Florida State College for Women" from about 1905 until 1947 when they became Florida State University. They had once been simply "Florida State College" and played college football including games against Georgia Tech until the Buckman Bill in the State Legislature made them one of the best "girls' schools" of that era. UF opposed the creation of FSU's football program saying there were not enough HS players in the state to supply both state programs.
Another interesting retrospective is 1959's proposed "Airplane Conference" (under section 1.1 below) which was ultimately vetoed by the service academies:
https://en.wikipedia.org/wiki/Superconference