It'd be nice to know the Make/Model/Size of the RV. If it's a small to mid size Class C on Ford...
The Firestone Transforce seems like a good tire and one that can be bought at a discount price. I'd call it equivalent to Michelin LTX-MS/2
Speaking of Discount, Discount Tire (America's Tire in the West) will do RV tires no issue. Some big boxes like Sam's Club won't.
Ford doesn't suggest rotation on rear tires. I rotate Spare to Left Front, Left Front to Right Front, Right Front to Spare. More on that to follow...
This is my opinion, but I believe the Right Rear Inner leads the worst life of all the tires. It's in out of the air flow, so it runs warm. It also carries a little more load than the outer if the road is severely crowned. So does the Left Inner, but: At least on Ford, it's close to the hot tailpipe, and worse, the Right OUTER gets run off the edge of the pavement. When that happens, the Inner takes the full right rear load.
Tires never forget an offense. When that inner blew, the outer was suddenly and severely overloaded. May have looked OK, but it was angry and you were gonna pay.
Here's what I'd do:
Round out your set of new tires. If you have two new but different ones, either use both on the front or get a matching one for the front and make the other one a spare.
I think you should have a spare, and that spare should be a young tire. Our prev owners never used the OEM spare, and I scrapped it when we bought 07 new tires. Still had mold marks, factory label, never on the ground. That's why I rotate the spare with the fronts. Would rather mount a spare that was young and had been driven than one that was young but never on the ground.
You don't want to mount a spare and have it fail in 50 miles because it was aged out and you have 100 miles to go!
Put custom valve stems on your four rear tires and 02" metal stems on your fronts and spare. I have Borg (Dually Valve) and those are the least expensive option right now. That's thanks to Camping World selling them now at a very attractive retail price, and they often have sales/specials/coupons. The more expensive Tire-Man sets are the same stuff. Not a bit better. Both Bill FalkenBorg and Chuck Carvitto are great guys with good products. I bought Bill's Dually Valves because that's what a shop (Six Robblees) was carrying and the price was very good. Either will give you great performance, better than just about any other option. Just put GOOD STEMS all around!
All the LT225/75R16 tires carry the same Load and Pressure Ratings. Even if your coach is lighter like E350 chassis, you'll probably end up with the Load Range E tires rated to the higher axle load of E450.
If your coach isn't maxed out on weight, I'd say get LTX, TransForce or the like. If you know you're at max axle weights, like we are, then consider a "commercial" tire in that same 225/75R16E size. The Michelin XPS RIB and Bridgestone Duravis R250 come to mind. They aren't rated any higher, but are built to be a little tougher. I'd heard the LTX tire in 225/75R16E has been reinforced with an extra steel ply. Might be worth investigating.