Look at the GVWR on the yellow sticker on your trailer. That is the max weight for your loaded trailer. Then multiply that number by .15, which will be the calculation for max tongue weight on your tow vehicle. (The number you quote is the empty trailer - no propane, battery, or gear.) You will be surprised at how much the "stuff" you load in the trailer actually weighs. (I suggest going to a scale to be accurate.)
Now take the max tongue weight calculation and use that as one of the factors in the determining the payload for your tow vehicle. There should be a sticker inside the door of your tow vehicle that tells you what the max payload is for that vehicle. The payload consists of your tongue weight and the weight of all passengers and anything else you load in the vehicle (including the weight of the hitch and equipment). This is the number that should be of the most concern for you. I'm guessing you will be over that on the F-150. Not sure about the Expedition, but it is also a 1/2-ton. The towing capacity rating is how much of a load the power train is designed to "pull." The payload capacity is how much the vehicle can safely "carry" and control for that suspension. Two different things!
2015 Jay Flight 32RLDS Elite
2012 Chevy 2500HD Crew Cab LTZ (6.6L Duramax/Allison)
Equalizer Hitch (1200# bars)