I'm not fluent in addressing 5th wheel pin weights (I'm a TT guy), but I believe that 15% to 25% of the 5th wheel's "loaded" weight is the recommended "loaded" pin weight. The Eagle 313RKS has GVWR of 14,000lbs, so if we were to take 20% (middle ground) of the GVWR this would give us a 2,800lb loaded pin weight
. Now, not everybody tows at GVWR, but this will put you in the ball-park. Also, the published dry hitch weight of the 313RKS is 2,345lbs, but who tows an empty 5th wheel!
What I would do is take your 2500HD TV "loaded" with full fuel, passengers, cargo, etc., to a CAT scale and weigh it. If you don't have a hitch installed yet, add this weight to the CAT weight. Take this total weight and subtract it from your TV's GVWR......how much do you have left to work with
This is a simple way of looking at it, but more importantly the TV's axle weight limits would also have to come into the conversation as well. IMO I wouldn't attempt to tow it with my 2500HD 6.0L gasser....., maybe a 8.1L gasser...., but the DuraMax/Allison would do just fine if the weights work out.
Maybe some of the 5th wheel forum members will chime in with some "hands-on" knowledge and we can both learn something.