Don't know if this will help, you've probably already seen it. Hope you followed all the guidelines:
Towing guide for 2016 ExpeditionWonder if the 2016 model is simply more light weight than your 2005 model?
Tires could be under inflated.
You might have to shift some weight in the camper further forward (tail heavy)?
Did your new Expedition come equipped with the factory installed tow package or did you simply add a hitch? If it was not factory, it's possible the suspension may not be adequate for the weight of the trailer you're towing. (I don't know how Ford does this).
I'm just grasping as straws here, but from your description it just sounds like the tow vehicle suspension is too light.