IMO, Casey was not capable of carrying Caylee's body for any great distance while carrying a full-size shovel for burial.
Think of carrying a 3 year-old child fast asleep on the sofa, lifting them up and carrying them to their bedroom, and also add a full size shovel, which is heavy, and you personally weigh maybe 100 pounds.
A sleeping child is like dead weight as they are out for the count while sleeping.
But in this scenario, you have to carry the sleeping child perhaps a 1/4 or 1/2 mile while carrying the full-size shovel in order to get to your house. Your house though is about a 1/4 of a mile off the road, through the woods.
It's easy to test this out, just by going to a Pet Store and pick up a 35 pound bag of Dog Food and carry it through-out the store a few times, then out to your car and be at least 100 pounds with absolutely no upper body strength. Oh, don't forget to bring a shovel with you as you need that too!
Or if anyone has a 35 pound dog, pick the dog up and carry the dog with both arms and pick up a shovel and start walking, but you again have to be about 100 pounds in weight!
The only way Caylee is deep within any of the areas TES has been searching, based on LE thoughts, is if someone much bigger and stronger then Casey carried Caylee.