More truck stuff...
Susan,
If the pre-owned F350 has the "new" motor, then it should be rated at 23,000 lbs GCVWR.
The best bet would be to weigh the truck at a public scale, to get an accurate figure for towing. Let's say the truck in it's normal configuration weighs 7500 lbs (2 people, tool box, golf clubs, trailer hitch, full fuel, etc), then 23,000 - 7500 would yield a "towing" capacity of 15,500 lbs.
The Golden Gate has a nominal Dry Weight of 12,500 lbs. Plus, you need to add in the weight of any additional options. Then food, clothing, other goodies. Maybe a couple of bikes, hiking gear, boots, "stuff" in the basement storage, like barbeque, extra propane tank, chairs, table, ladder, spare this 'n-that, and now your current weight sits around 14,500 lbs.
We haven't talked about water yet, but this is one item that can easily be managed. And, it should be, as with all tanks full, you would suddenly weigh 1500 lbs more. Right at the 16,000 lb "rating". But if your grey/black water tanks were flushed before travelling, you could still carry an almost full tank of fresh water, if you wanted (or needed).
But, I've been wrong before, so the safest thing would be to know your actual numbers.
Hope this helps...