I'd tow that with my 12 Ram 2500 CTD. RAWR is 6000lbs My empty rear is 2950 with the B&W installed. That leaves me with 3150lb for the rear axle. I currently tow a 9000lb 5er with an 1800lb loaded pin. My dry pin is 1385lbs so I added 415lbs to it. Apples to apples I'd add 415lbs to the 293's dry pin of 2075 for a total of 2490lbs. That would leave me with 5440lbs total. I'm also RAWR limited at 6000lbs because of the 245/75/17 tires. Get an SLT and that goes up to 6200lbs. Put 18" tires on and the RAWR will go to 6800+lbs.
No it won't change the door sticker. For me that's not an issue. To others it may be and it's something the OP needs to address.
FWIW the 2013 2500 is an improved 2012 3500. Same exact rear springs as the 12 3500 along with the improvements made to the CTD and tranny.
Ironically a guy over on IRV2.net had a similar issue recently. He bought an F250 and a larger 5th. Both were suggested by the Ford dealer and the RV dealer. He then found out he was over his GVW by 7-800lbs. After he picked up the 5th and towed it quite a distance home, he came to the conclusion that it was fine. Most of the time he never noticed it was there. He also had air bags installed prior to towing.
