When I buy a trailer with 13" tires I always sell them and go with 14" or 15" tires all depending on how heavy the trailer is. Not much in the way of quality 13" tires.
As Steeljag says 13" LT tires are non existant. And the LT sidewall is just as stiff as a ST...guess this internet myth will never die regardless of what actual tire experts tell us.
Not all Maxxis ST8008 has the nylon cap under the tread. Better check with Maxxis before deciding on a tire size. The cap helps hold the tire together as it side scrubs around corners. These tires are speed restricted to 65 mph.
I would look at ST tires like the new Carlisle radial trail RH and the newer HD series tire. These tires carry a higher speed rating similar to a LT tire.
Or the Provider ST tire which has the nylon cap and is M speed rated