Haven't heard of Maxim unless you meant to say Maxxis. We use Maxxis ST tires and they have performed well hauling our 32' 10K# rig around. Obviously, a heavy duty LT tire will provide the best longevity and towing experience, but for rigs around 10K# and under Maxxis is the best choice if staying with ST tires.
Going to a LR-E 15" tire from a LR-D tire is a good thing as long as your rims can handle the 80psi required. Not a good idea to overload rim psi or under-inflate a ST tire if rim is not capable of 80psi, a ST tire will overheat when not inflated to max psi stated on sidewall which is one of the reasons for their high failure rate. Discount Tire didn't have them in stock, but they ordered them and had them ready to install in a couple of days.