First, there ought to be a tire placard somewhere on the vehicle. I've heard it is common for that to be near the driver's front corner. What does it say for tire size and pressure? Use that as a first step.
Second, it would be good to weigh the trailer - individual tire weights if possible - if not, at least axle by axle. Then you need to add a factor if you didn't get individual tire weights - 7% if axle by axle, 12% if all axles together. Then compare that to the load carrying capacity of the tires. I am of the opinion that tires should be loaded to more than 85% of their capacity at the pressure used.
You never told us what tire size you have so I am wondering why anyone would think they could give you advice! Mix of LT's and ST's, yes! But are the numbers even the same?
I am going to suggest you prioritize getting all the tires replaced. You're in Southern California, and the sun can really take a toll!