YES, Go to Load Range E! Actually, very hard not to. That size is almost always sold in E, just be sure they're LT (Light Truck) designation. There are "P" series (Passenger) tires in that 225/75R16 size.
Anyhow, get E, and weigh your loaded coach. Set tire pressures according to weight. Put good VALVES (nothing rubber!!!) on there. The least expensive kits are sold at Camping World and will do the job just fine. Custom made, of solid brass. That's for the rear. For front and spare, all you need is ordinary 2" METAL valves.
Goodyear, Uniroyal, few users, limited reviews. A Michelin tire needs no introduction anywhere in the world. The LTX series (again must be "LT") is popular original equipment. Many of us have gotten Firestone Transforce and those comments are good. Michelin XPS and Bridgestone Duravis R250 are premium "rib" treaded tires and most consider both to be excellent. I use R250.
Hope this helps.