If it were a design problem, Coachman would have issues with all of them.
Tongue weight may only be part of the problem. There are several other possible contributors. It could be a combination of more than one of them.
Things to check / look at:
1. Tow vehicle payload - F150's are not all created equal. There are versions of the F150 that do not have the payload and tow capacity to handle that trailer, and, there are versions that could handle it and more. Ford is not alone in building vehicles this way. Maybe, your particular F150 is one with lower capacities, and could be at or near it's max weight.
2. Tow vehicle tires - Are they "P" rated tires inflated to pressure specified on drivers door sticker? If so, there could be sidewall flex contributing to the trailer sway. Tire pressures listed on door sticker are not max pressures for the tire. They are normally a bit lower for passenger comfort. The fix could be increased tire pressure, or, upgrade to "LT" tires.
3. Improper hitch set up - Trailer should tow slightly nose down. Front axle weight restoration should be at least the amount recommended in the tow vehicle owners manual. Some manufacturers recommend 50 percent, some recommend higher.
4. Trailer tires and wheels - Are they inflated evenly and to specs? Are they balanced? Any bent rims?
5. Trailer brakes - Check for a brake hanging up on one side or the other.
6. Trailer axles - Are they aligned? Maybe a bent one?
7. Trailer wheel bearings - Got one getting ready to burn up from lack of grease? Do all the wheels spin with same amount of friction?
8. Trailer holding tanks - As mentioned above, one or more of the holding tanks may be located in front of the axles, specifically to offset weight from toys.
Spend enough time reading posts on here, you'll see RV sales people are more famous for telling customers "sure you can tow that", than for saying "you might want to look at smaller trailers or bigger trucks".
Manufacturers work the same way. If there happens to be one half ton truck that, under the right circumstances (no passengers or cargo), could tow a particular trailer, they will advertise that trailer as being half ton tow able.