Going via Montgomery to Disney adds an hour to the drive from Middle TN to Disney (per Google Maps). I had planned originally to over night in Tifton, GA. Looks like Dothan, AL may be the better option. It really depends on what times are scheduled for the games. If they are noon games, they most of the traffic will have died down by the time I would be getting into the area. If they are afternoon/evening games, well no way am I going to be on I-75 via Atlanta.
Time to start researching hotels in Dothan...