I've been checking door jambs on the f150s with the 7000lb package. XLTs are about 1900 payload, Lariats without a sunroof about 1750lbs payload.
Also, those payloads already take into account a full tank of gas (36 gallons on some of them), so you can subtract out your 200lbs for gas.
You should be within your limits and obviously could move some of the random "250lbs" to the trailer. IMO any setup should be weighed. Ideally when brand new and empty, and then again when loaded so you have an idea of how the loading affects the tounge weight.
Even better when the tanks are new and can be dumped anywhere, fill each up varying amounts and see how each tank affect the tongue weight. If a 1/4 full black tank removes 40 lbs from the tounge, you know that would offset about 50 lbs of firewood in the front storage compartment just as an example. A consistent tounge weight will work best with your WD hitch dialed in. A battery and full propane alone will add about 120 lbs to the tounge before loading anything in the garage or bedroom.