Using P or LT tires on a single axle trailer or a liteweight multi axle trailer is perfectly acceptable. In fact thats all we had for years before the tire industry came up with the infamous ST tire.
A 3500 lb trailer has approx 875 lbs on each tire. You sure done't need a E tire on that trailer any P or LT in your wheel size will work fine.
I keep P tires on all my single axle trailers up to 3400 lbs I have one 14" tandem axle car hauler with derated 3500 lb axles that I keep P215/75-15 BFGs on it. These tires has thousands of miles up to 75 mph legal speed.