If your unit is a 2011 HL Elkridge 29RKSA you should have ST235/80R16E tires as OEM
As you stated your dry weight should be (lbs/kg) 9664 / 4383.6 and your VRWR is GVWR (lbs/kgs) 14075 / 6384.4
You have no obligation or regulation to stay with ST tires and every reason to switch to any of several quality LT tires. Bridgestone Duravis R250 or Michelin XPS Rib's are 2 of the most frequently purchased and recommended LT tires for unit with your GVWR and GAWR.
Do not fall for the ST tire hype and BS that will be along shortly I'm sure.
Another option is to move up to a G-rated tires if your RIMS are rated for 100PSI and then the 2 most recommended tires seems to be Goodyear G614's or Sailun S637's.
