Atlanta Journal Constitution article from 2014 on the 50th anniversary of Tech's Departure.
This vote took place in January 1964. Tech's last football season in the SEC was 1963. Tulane left a couple of years later. Into the late 1980's Tech continued to schedule Auburn and Tennessee annually on the gridiron.
While I appreciate Dodd's recruiting integrity, it did not help his cause that he refused to play the Mississippi schools. Back then each school could choose which 6 SEC schools to play each season, with no mandatory rotation at all.
Georgia Tech and Mississippi State did not meet in football at all during Tech's 30 years in the SEC. Tech played Mississippi twice during their time in the league - a regular season contest in Atlanta in 1946, and the 1953 Sugar Bowl (the bowl likely matched up those two to keep things lily-white).
And Tech was not alone. Vanderbilt and Auburn did not meet in the regular season at all from 1952-1977. They did meet in the 1955 Gator Bowl (wouldn't surprise me if race was a factor).
Basketball operated then much like it does today - you had your "permanent opponents" with whom you played home-and-home annually, and the rest you played once a season.
But Dodd had "national aspirations" for Tech. That didn't work out too well. I wonder if he was forward-thinking enough to consider that major league professional football (NFL or AFL) would likely expand to Atlanta in the next few years which could dampen independence. USC wasn't paying attention 7 years later to see how well independence was working for the Jackets.
But yeah, if Dodd was really interested in staying in the SEC with decent recruiting guidelines, IMO he would have agreed to start scheduling Ole Miss and Ole Miss State in exchange for their support on the 140 rule.
