It is very hard to comment without knowing the contruction and use regulationes which apply to the vehicle combination nor the actual specification of the braking system fitted by the manufacturer for the Australian market. It is very likely different in some way to the European spec. AFAIK a USA spec tractor unit used to include a bobtail valve, manually operated from the cab and selected to reduce brake pressure when running solo. The trailer spec could be something completely different to the European normal, modern trailers’ EBS systems take into account whether drum or disc brakes are fitted.
In this country you would be subject to an immediate movement prohibition with those taps fitted and a subsequent full annual vehicle roadworthiness test. The fitment of the load proportioning valve as shown and described worries me, I cannot see how this valve can relate its output to the weight imposed on the trailer axles. All it can do is deliver a reduced pressure to that which supplies it. Even if its control pressure was taken from the unit’s drive axle chamber pressure it would still not have any relationship to the load (mass) imposed on the trailer axles. Many (50) years ago pressure regulating valves were fitted in the trailer circuits on the tractor unit, but certainly not recently.
If your problem is not a mechanical issue with the trailer brakes, then it is excessive air pressure delivered to the trailer brake chambers in relation to the bogie load. The brake balance between unit and trailer has long been a problem with a history of different solutions. From waht you say it appears that the trailer does not itself have any means of regulating the air pressure at the chambers in relation to the axle load. The best advise I can give you is to contact the makers of the air brake equipment fitted to the trailer for help.
I realise this does not answer why two other units do not lock up the trailer brakes, which is why from the information given I had suspected the footbrake valve was not acting progressively in relation to the effort exerted by the driver’s foot - actually a common fault. However you seem to have eliminated that possibility.
To give an example of how things can go seriously wrong between vehicle markets and specifications I will relate the story of what happened locally in 1986. An unladen artic went out of control when the driver applied the exhaust brake in a busy urban situation. It turned out that the German made unit applied the trailer brakes when the exhaust brake was operated (the Dauerbremse system), the trailer brakes locked up and the trailer mounted the pavement. Tragically this was at school chucking out time and three primary school children were killed.
Edit: add link to Commercial Motor article banning the system mentioned .