He wasn't trying to force them to change. He tried that when he was there and it failed - complete with Bear Bryant double-crossing him. Leaving the SEC was always plan B, but they showed they were intransigent. He had no choice. Leving wasn't to make them change, it was because they refused to change.
The plan (plan B) was to go independent and play a national schedule so he could recruit nationally. If you look at the post-1964 schedules, he replaced Florida with Miami and added Navy. In 1965 he swapped Alabama for UVA, and the old Florida spot became TAMU, plus Navy. In 1966, Penn State, UVA, and TAMU were all on the schedule. In 1967, it was TCU, Tulane (who had become independent), Miami, and Notre Dame. By 1968, we only played UT, Auburn and UGA from the old SEC schedule and the new opponents were TCU, Miami, Tulane, Navy, and ND. In 1969, it was SMU, Baylor, Southern Cal, Notre Dame, and Tulane. In 1970, we picked up South Carolina, FSU, Miami, along with Tulane, Navy, and ND. In 1971, it was Michigan State and Army, along with USCe, FSU, Navy, and ND. 1972, he added Rice and BC, and in 1974 he added Pittsburgh. You saw us playing in Texas (Rice, SMU, TCU, Baylor, TAMU) and Florida (Miami, FSU) a bunch, plus the Midwest (Pitt, PSU, MSU, ND). Dodd's plan was to recruit nationally.
So, what happened? I think the money dried up and Tech hired a Pres who didn't like football... all at the same time as conferences began to sign tie-ins to bowl games. and reap the reward of those games as they began to proliferate. In 1964 there were 9 college bowl games: Rose, Cotton, Sugar, Orange, Gator, Sun, Liberty, Bluebonnet, and Tangerine. By 1974 there were 11, and by 1978 there were 15. Money was starting to flow into the conferences and Tech was becoming closer to bankruptcy.