I agree with
@smeagol that you do not have enough WD tension. On any WD hitch, there's significant tension necessary for it to do it's job of transferring hundreds of pounds across the length of the car. On the Anderson, there will be more tension still because of its horizontal tensioned architecture.
There isn't a thread count to shoot for as every setup will be different. I remember i had 7 threads showing on my previous setup.
Go up 2-3 more threads. If it's working, go one more still, and one more again, until you find diminishing returns as you can always back off easily enough.
To hitch, you should be in AHC High and/or use the tongue jack to lift the ball up higher than ride height. At that point, you should tension the chains to be rather tight. Then lower AHC to Normal and/or full retract the tongue jack. There should be no slack and significant tension in the weight distribution chains.
The red bushings should show some good compression/bulge (image from Andersen's media).
View attachment 4003983
AHC should not be a compromise with bounce unless there is a mechanical issue.. Static suspensions aren't a band aid either for not enough WD tension, as there you'll be dealing with the same seesaw, but with more squat, and a less comfortable ride.
Depending on your tongue weight, it is wholly possible the Andersen doesn't provide sufficient weight transfer. Without that, the rig works as a seesaw about the rear axle. You need enough weight transfer to the front axle to get out of this seesaw equilibrium where it can't decide which way to take a set hence the bounce.
As mentioned earlier, you might want to modify the drop hitch to bring the ball in closer. As that gives the tow vehicle more leverage (weight on one side of the seesaw), requiring less WD tension for it to find its happy place.
Maybe take a picture of your tensioned setup at ride height, particularly of the red bushing. What is its free length versus tensioned length?