In my experience, I've seen 4 primary causes of trailer sway.
1. downhill and trailer is pushing the truck, but this is downhill only and exaggerated by other less than ideal conditions.
2. Soft trailer tires.
3. Not enough tongue weight. (Doesn't appear to be the case here)
4. GROSSLY overloaded tongue weight on the truck (not the case here).
Certainly there are other nuances that affect sway too but I think these are the more typical ones.
(Like axles too centered on trailer, enough tongue weight, but a disproportionate amount of load behind the trailer axles will make the tail wag the dog.)
OP, agree 50psi in the trailer tires sounds very low and squishy trailer tires will cause or exaggerate sway.
Presuming your 80psi tires are 15" on 5200lb axles (just a guess unless your trailer is overbuilt), you should be near max pressure for the load.
Also, have you tried towing without the wdh or taking most of the weight distribution out of it to eliminate that variable?
Agree, that tongue weight and truck setup should tow fine.