Weigh the trailer, then look at the load charts for the E rated tires. Chances are, you will not have to inflate them to the maximum pressure shown on the tire sidewall. Remember, that pressure (80 PSI?) is for the MAXIMUM LOAD the tire is designed to carry.
If it was my trailer, I would throw away the ST tires, put LT Load Range E tires on it, inflate the tires to the pressure required by the load, and go happily on down the road!
A simple and relatively foolproof way to get the inflation right is to use the "Chalk Test". On a clean, hard surface (a paved parking lot, etc.) make a chalk mark across the tread of the tire. Drive a ways, then look at the chalk mark. If the mark is worn off mostly in the middle, the tire is overinflated for the load. If the mark is worn off on the edges, the tire is under inflated for the load. If the mark is worn off evenly across the tread, the inflation is just right.