I agree that an LT tire is the best tire for replacement but you say you want to stay with the ST tire. I have not read of many ST tires that are not problematic. The Maxxis 8008 as stated seem to be the best but can be hard to find, especially if away from home and in need of one quickly.
Regardless, IF you decide to go to a LT tire it MUST equal or exceed the axle rating of your trailer. An LT tire in the weight capacity you would need may create clearance problems and require a higher rated rim because of pressures.
2013 Crusader 330 MKS
2013 Chevrolet Silverado LT 2500 D/A