2012 Ram Diesel 6.7 Tow Capicity

well it's not too hard to figure that you'll be over every tow rating with that 5er. If you use the RAWR and throw some bags and higher rated tires then you'll cover the pin weight. But you never cover the tow rating.
One thing to think about is that your 2500 is a 3500 with just a different spring pack. If you use the 3500 as a bench mark then you'd be close but good.
I know with my 12 Ram 2500 CTD that the tow rating jumps 1000lbs by going to the same model 3500.
I think Ram rates their trucks on cooling as well as frame and suspension. if you look at a 13 2500 I believe the only thing they did to the suspension was add the 3500 springs. But they improved the cooling and some other mechanical things and the tow rating really jumps. So IMO it's more about how hard you want to push the truck rather than can the truck handle the 5th wheel.
Interesting to note that the 13 2500 tow rating jumped to 17,300 with the standard 3.42 gears. That alone tells me Ram reworked the cooling big time.

Well once again the Catch 22 of a 250/2500!

You are asking a question that in reality only you can answer, the question is do I feel comfortable towing beyond my trucks 10,000# class restricted GVWR and go by the trucks rear GAWR.

No matter how you answer that question you first need to fill your fuel tank load up the family and head for the scales to find out what you have for payloads(s).
I stated payloads one is based on the 10,000# class restricted GVWR. The other on the difference between what the truck scales and the VIN sticker listed rear GAWR.

The 12,650# towing limit is a rating based on power and rear gears. Not sure if Ram still has the placard in the glove box with the trucks gear ratio. if it is like 3.42 that could be the reason for the low max trailer weight.
Keep in mind was the last year before RAM got aggressive with towing numbers. If you have an automatic transmission I would be careful, chipping, be safer putting in either 3.73 or 4.10's
But once again Your Choice your money.

Until you weigh your RAM (fully loaded) you'll not know it's actual capacities such as remaining payload, and remaining GCWR.

The payload sounds about right for the diesel, but the towing should be more than 12,650. You will likely need air bags to level the load. You would have to weigh the truck full of fuel passengers, gear, to see what you have left on your RAWR/max tire rating.

The loaded trailer could have a pin wt near 3,000 lbs, plus hitch wt about 200. If loaded rear axle weighed 3,000, you'd have to subtract that from your RAWR.

Jerry