The short bed is a concern which may or may not be overcome but I don't see how you get over the cargo capacity issue iff your truck is a 8800 lb GVWR,
My F-250 long bed extended cab weights 7200 with a tonneau cover and a tank of gas. You have short bed but crew cab. For benefit of doubt, say you are 6800 lbs with a tank of gas, that's a 2,000 lb cargo capacity. Say you only load the 5er to 8,000 lbs, that's stilll 1,600 pin weight (20 percent). You only have 400 lbs for your large family. Putting gear in 5er over truck helps but you will still increase the pin weight.
You need to weigh your truck with a tank of gas and establish a base weight and go from there but I don't think you'll like the answer.