OK, don't see any brochures for Fun Chasers, so I have to take your word for the tire size. If the tire is rubbing the top of the wheel well, the axle (if it's a torsion axle) may have collapsed, or, if the trailer has spring mounted axles, they may have weakened, allowing the trailer to "settle". These problems can be rectified and you should do so.
As long as the tire size is the same as OEM, it does not matter if you go with Load Range C or D, it does not change the tire radius. But, as you have reasoned, Load Range D is a better choice.
I'd repair the springs or the axles.