ATL is actually farther than half way.
If you leave early evening, plan on getting to ATL about 12 hours after you leave. SO if you left at 4pm, you would get to ATL about 4 AM. not the time to be checking into a hotel unless you plan on checking out by 11am. If your set on staying around ATL I would leave earlier in the day.
We always do the drive straight thru, but understand that is not an option for everyone. So I would look at your departure time, and add 12 hours to figure ATL arrival. Then plan on about 8 hours from ATL to WDW.
AN option might be leave at midnight, try and drive to the FL state line or Valdosta, get there early evening. Get a good night sleep and then your only a 3 1/2 hour drive or so from WDW Sat Morning.