Hi hotqld
Although my van is lighter then yours (2000kg ATM & ball weight 200kg) I experienced a similar issue on the development roads in outback Qld last year.
I found that if I removed the WDH the “Bounce” was greatly reduced.
I like the WDH as I feel it returns some of the positive feel to the steering and reduces sway when a truck goes past so I refitted the hitch but reduced tension on the chains.
I remember reading somewhere that each full link after the tension is placed on the rod(Long arm) displaces approximately 20kg.
As for air bags, if you are running standard suspension I would say yes, use the air bags to level the Jeep and the WDH to return steering control.
I have had heavy duty springs fitted (CRDSTU made by King Springs) and the rear end sag is limited (about an inch) and it sits level.
I would also check your tyre air pressures as a lot of people over inflate the tyres on there grand, factory recommended pressures are only 33psi.
When towing I run 33psi in the front and 35psi in the rear. After an hour on the road I re-checked the pressures and the front where 36psi and the rear where 39psi.
I used the on-board tyre pressure system to check the pressures.
If your pressures are to low the psi increase would be greater then 4 psi (which is considered normal) and you would need to add more air.
Over inflation gives a firmer ride and wears out the centre of the tyres prematurely.
If you choose to replace the springs do both the front and the rear, you won't be sorry as the handling is greatly improved over standard.
I am not saying that this is the solution to your issue but it helped for me.
Ps
My hand book says the max tongue weight is 327kg. Is yours a Hayman Rease towbar or factory?
Dave