Six Flags Over Georgia is my closest park and I'm a season pass holder. What safari are you near? Regardless, I would put AK as my last choice unless you were doing park hoppers. If you do another park, I would highly suggest Hollywood Studios as Epcot isn't much of a kid park. If they are too young for thrill rides though, maybe consider AK or Epcot.
Plan on getting to MK 30 minutes BEFORE rope drop. Transportation into the MK is tricky and takes longer than you might expect. And if you end up even 30 minutes late it will make a huge difference. You can knock out about 50% of the "must dos" before noon if you are there at rope drop. It's rumored that FP+ for off-site guests might be available this week. If so, that will help you a lot.
If not, go to Peter Pan first and then find a kiosk to make your FP+ reservations. If your kids are old enough for all the thrill rides, I would try to reserve Big Thunder Mountain, Space Mountain, and either Haunted Mansion or Pirates. The next choice would be Jungle Cruise. Splash Mountain will have pretty low waits this early in the day. If you make Big Thunder your second ride, I might even skip it for FP reservation. If your boys have an interest in Enchanted Tales with Belle then make that first priority over Space and Big Thunder.
If you are going to do the Tiki Birds, Country Bears, Carousel of Progress, People Mover, Hall of Presidents, Rail Road, or Tom Sawer island save them for 1-5 PM hours. And stop for lunch either by 11 or after 2. I prefer after 2 because I don't like stopping while the lines are still relatively short and I can wait.
Rides I would consider a must do (in order) that I haven't already mentioned are:
It's a Small World
Dumbo (strictly nostalgic purposes)
Tea Cups (same as above)
Winnie The Pooh
Buzz Lightyear Spacer Ranger Spin
Mickey's Philharmagic
Monster's Inc Laugh Floor
Tomorrowland Speedway
Stitch's Great Escape
Prince Charming's Carrousel
That's roughly 24 rides/attractions. At a commando pace I think it's possible to do most of them. If you want to see parades it might take away from a ride or two, but I believe the FoF parade is during the 1-5 hour so it shouldn't take away form the must see rides. If you want to see the Electric Parade and Wishes that will take away from some late night ride time (about 2 hours)
I hope this helped. Just make sure to keep the fastest pace on the first 2 and last 2 hours of the park hours. Those are the lowest wait times. Take it slow the rest of the time, especially the 1-5 hours.