Having a Ram 1500 Outdoorsman with a similar set up the truck is rated at a 10,500 tow rating..but for Rams, it is that payload that always gets you. Mine is high at like 1650 lbs but when the 32 gallon tank is full (32 X 8lbs) and tow of us and the two 100 lb dogs and the winch bumper and winch on front, AND the 500 lb hitch weight. Well, you are there or over.
Your 700 Plus hitch weight surely is approximately 50% of your payload. So, at some point, you are placing faith in something other than numbers... That is a big load for that truck. On the flat, I might be OK with it if I didn't travel much. I would never do the Rockies with it... But that is my choice not yours.