CapriRacer make a good point on number of actual plies in a tires carcass. Even my load range E tire 10 ply rated have a 2 ply sidewall however the two plies are much heavier than a lower rated D or C or P tire.
Looking at the new 25' KZ Sportman trailer shows a 4800 GVWR which has a 1200 lb per tire as a minimum load requirement. Your P205/75-15 may have 1453 lbs capacity at 35 psi.
Years back we used 32 psi rated P tires on tandem axle trailers but at only 32 psi we also broke the beads loose when side scrubbing around corners (the tire bead comes unseated with sudden loss of pressure). If you stick with P tires look for one that carries 44 + psi. The higher pressures insure the tires beads stay seated. The beauty of P tires is their not speed restricted to 65 mph as the ST tire nor do they have ST tire reliability issues.
If your needing more sidewall strength the ST205/75-15 C load range is rated as a 6 ply at 50 psi at 1820 lbs capacity which should be within the wheels pressure and load capacities. I would stick with a radial on a highway trailer. Right now the ST8008 Maxxis has a better reliability record that all the other ST tire brands.