I think you might want to take your truck and get it weighed. You can not rely on the info Ford publishes. I had a 2011 6.2 F350 with the max GVWR of 11200#. I have a 2012 10 2CDSE Northern Lite and I was over my GVWR by about 500#. This was with a camper loaded weighed a little under 3820#. I think you will be surprised that you are going to be over the GVWR.
Take a look at
Truck Camper Magazine Buyers GuideThey show that camper when loaded will be 4385#.
This is the weight slips from my 2011 F350 CC 4X4
Total empty weight 7740#
Front Axle 4400#
Rear Axle 3340#
With the camper on it
Total weight 11560#
Front Axle 4460#
Rear Axle 7080#
This is without anyone in the truck. So I was over weight by 360#. Not to bad but I was over my rear axle by 80#. This is with a camper that weighs 3820#. You are talking at least another 500# of weight so you are going to be will over your GVWR.
You may want to get an actual weight on you truck before making a very big mistake IMO.