So to provide what you asked for........
1. You will run out of payload before towing capacity.
2. Is the 1600lb payload from the door sticker on your truck?
3. What is the dry weight from the yellow sticker on the trailer?
4. Have you added anything to the truck (i.e. Tonneau cover, running boards, etc.) which gets subtracted from truck payload?
5. The dealer tongue weight quote is the same as the Jayco website dry hitch weight which "does not include cargo, fresh water, propane gas, options or dealer-installed accesories"
Your tongue weight will undoubtedly be higher.
6. The 100lb Blue Ox hitch weight gets subtracted from truck payload
7. Since Ford includes full fuel and a 150lb driver in their payload you only need to subtract 350lbs for your family from truck payload.
8. You may want to research mounting the bikes on the trailer bumper. There are posts on these forums suggesting that without reinforcing the bumper that may not be a good idea. Ask me how I know.
9. Tongue weight should be 10-15% of trailer weight, mine is 12%.
10. The only way to get true weights is to run the truck & trailer across CAT scales, but that means you already bought the trailer.
Do the math and determine for yourself.
Personally I think that is too much trailer for that truck to have a 'comfortable' drive. I towed a 2017 Jayflight 27BHS with a 2008 Silverado 1500 and it towed OK but I wouldn't call it comfortable.
Good luck in whatever you decide.