Replacing the problematic ST tires with a LT has always been a excellent upgrade for eliminating ST tire issues for all types of trailer owners.
Your ST235/80-16 E at 80 psi are rated at 3400-3500 lbs capacity.
However which LT depends on your trailer axles rating.
A LT235/85-16 E 80 psi at 3042 lbs capacity works great on 6k axles.
If your trailer has 7k axles then tires like the Goodyear G614 or Sailun S637 are popular sizes in the LT235/85-16 G load range at 3750 lbs capacity and 110 psi.
Some folks with 7k axles on their trailers have moved on up to the 17.5" LT tires and wheels.