I've seen those rams also. Likely they're overweight at the pin and maybe for towing. We've got 36' Carbon, which isn't as optioned as the Cyclone or Montana - and it's gross is over 14k.
The fact is that your Ram will pull it just fine. Likely you'll hit the payload limit first, but 13.7k isnt' far behind. The issue will be stability, legality, and braking.
I can tell you that moving from a single wheel to a dual wheel ram makes a big difference... Or keep see if you can find something that is under 14k gorss and 2500 pin...
Don't know what state you're in - but the other thing to watch for is that many states require a different license for towing that much weight. Your RV dealer won't tell you.