I'm leaning towards you being overweight on the tires. Getting weighed would be a good idea. Load range C tires are lightweights. If you can, upgrade to 15" wheels and LR D tires if they will fit inside your wheel wells and there's no less than 3" between the tires. I don't think you can find load range E tires unless you go to 16" wheels which may be overkill for your trailer.
NEVER reduce tire pressure. It's almost always recommended to use the maximum tire pressure (on the sidewall) in trailer tires. Also, if your tires are speed rated to 65mph, don't drive faster than 65 because you'll overheat them quickly.