Good point. Extremely tall tires with soft wobbly sidewalls would be a likely disaster as you stated.
I didn't read the original poster's signature. He also lists Hummer wheels. Hummer wheels are probably not even rated to carry the maximum axle rated weights of a Dodge Ram 2500.
The OP's truck is simply not the right truck for any large and heavy toy hauler.
Its all about the tires on a SRW. OEM tires wheels are good for 3195lbs, H2 Wheels are rated at 3195 ( I have been told thats what they are stamped at), but I don't recall many LRE 315's, most are LRD 3195lb rated at 65psi. . You WANT 80 psi with that much weight...
HBarlow's original math is the key... RAWR on and Dodge SRW is based 100% on tires, as the axle is rated the same by AAM for SRW or DRW configurations, at 10,910lbs (Dodge rates the DRW RAWR at 9,350 lbs, so that tells me thats what they limit the brake, frame, and suspension for). Brakes, frame, etc are the same. So if you are going to be towing that much with a SRW you need tires to handle it, 19. 5's are the most HD, but some 18's may offer the weight rating you need. You probably want a tire/rim combo good for 4K per tire.
Add airbags and a good trailer brake controller and go to town while being safe.
It won't be as stable as a DRW, but it will support the load with some modifications.
Next is the legallity of it. Simple fact is the DOT only cares about what is safe, so making sure your within the limit of the tires, and States only care about what you pay for. . so pay for the proper GVWR. (I am legal to 26K GCW, even thou my OE GCWR is only 21K).
Your truck is OE rated for 11,850. But change the OE build to a 3500 SRW (which is the only difference is OEM overloads (airbags are better) and make it a 325/600 motor and your OE limit is now 15,750 which is what your trailer would weigh. . You just have to look at how much pin weight your tires can support. But 16K is only 250lbs away from what Dodge says your truck with 20 more hp and overloads can handle.
OE stuff
Dodge Towing Guide - By Vehicle Results
The bottom line is that you can't legally up the GVWR of a 2500, no matter what you do to the truck. On a 1 ton dually you can change the GVWR by putting heavier load tires on it, but not the 3/4 ton truck.
How on earth do you figure that? DRW Axle ratings are already lower than combined tire ratings.
You can't change the GVWR on ANYTHING in the LD truck market, but like I said States only care about what you pay for and DOT only cares about safety.