In the tire world, replacing tires that do not conform to the vehicle tire placard is called Plus Sizing”. Unless your trailer’s manufacturer has recommended optional sizes you’ll be on your own in your search for new tires.
To go from LRE original equipment tires to any of the LRG tires you have mentioned will almost certainly require new wheels. Some of the LRG tires have a minimum wheel rim width requirement of 6.5” and all will have maximum inflation pressures in the 110 PSI area.
The least expensive option will be one of the many ST235/85R16 LRG tires available from the China tire builders. I’m just guessing here but I think the easiest ones to find will come from one of the newest ones on the market from Carlisle. They probably have the widest range of USA distribution centers and retailer participation.
Here is their link;
Their ST235/80R16 LRG is not considered a “Plus Size” because it conforms to the same load inflation chart as your OE tires.
All of the ST235/85R16 tires are going to be about an inch taller than your OE tires. It’s an area for you to insure has the clearance for taller tires. Trailer axles are notoriously installed very close to each other and an inch can affect the “go no go” fitment parameters.
NOTE: I’m not recommending a brand, I’m just presenting an option.