A properly built, properly loaded trailer should not sway, even without any kind of anti-sway hitch.
If it does, find out what is wrong, and fix it!
If there is not enough tongue weight, the trailer will sway. Fix it!
If the trailer is nose high on the hitch, it may sway. Fix it!
If, as stated, the tires are properly inflated (that does NOT mean they are inflated to the maximum air pressure, unless they are also carrying the maximum load), then the problem is very likely too light on the tongue, or too high in the front.
A last resort type thing would be to trade the tongue type trailer for a fifth wheel, then sway will never be a problem.
Good luck in finding out what is wrong, and fixing it. IMO, an anti-sway hitch is a band-aid, trying to cover up a problem that needs to be fixed.
CM1, USN (RET)
2017 Jayco TT
Daily Driver: '14 Subaru Outback
1998 Dodge QC LWB, Cummins, 5 speed, 4X2
2 Kawasaki Brute Force 750 ATVs.
Pride Raptor 3 wheeled off-road capable mobility scooter
"When seconds count, help is only minutes away!"