Load G tires (4080-4400 lb capacity) are better suited for heavy loaded 7k axles.
What size axles does your trailer have ??
What size and load range are your OEM tires ??
As was mentioned a 10000 lb trailer can have a 2000 lb hitch leaving 8000 lbs on the axles or 2000 lbs per tire. Now add the 10-15 percent reserve capacity = 2200-2300 lb. No way you need a 4000 lb rated tire for a 10k trailer
Tires on your trailer should have been selected by the trailers axle ratings plus a 10-15 percent reserve capacity. Trailers unlike our trucks can have too much tire for best wear and long term reliability.
The new gen ST tires are rated at 75-81 mph. As long as the tires are pumped to max sidewall pressures they can handle heat issues caused by speed....and Running a lower pressure in the tire can cause it to run hot which leads to throwing the tread belts or interply shear while making those sharp turns backing up or going forward.
We have some very good LT and ST tires out here for specific sizes and loads. Give us some numbers to work with.