Here are some things I've come up with myself:
1. Weigh the batter to make sure all the layers are the same size.
2. Use even bake strips so the layers will be nice and level.
3. Pipe the filling to make sure all the layers of icing are the same thickness.
4. Maybe insert one dowel in the center of the cake to make sure it doesn't slide around in transport?
In my many google searches, I've come to realize this cake turns out either really amazing (like the one on the Whisk Kid site) or reallllllllly bad, like this one... So any tips and ideas would be greatly appreciated!