The P tire on a single axle trailer is a excellent move. Their very popular with the boating crowd and other PUP owners.
I use them a small 12' tilt bed flat deck trailer with a 1750 lb axle. I also use 15" P tires on a tandem axle trailer. Their not speed restricted as the speed limit on the interstates around here is 75 mph.
Yes a P tires capacity is reduced per fed regs... S4.2.2.2 When passenger car tires are installed on an MPV, truck, bus, or trailer, each tire's load rating is reduced by dividing it by 1.10 ...... .
FYI in case you didn't know your ST185/80D13 is a bias ply tire and not a load range D at 65 psi. The D at that spot is a bias ply designation.
Maxxis has a couple of 13" commercial grade LT tires in the U-168 Bravo. Check them out to satisfy your wheels pressure and width requirements.
good luck on your search.