Why all the doubt with F150 Ecoboost? Is this 2010 again?
It's been out for 3 full model years in the F-150. Ford sells about 40$ of F-150's with them, so 250k per year! Plenty of feedback.
OP, payload is likely your limit, not the tow rating. 6300 dry means about 7500 pounds loaded with 900-1000 pounds of loaded tongue weight. Does your truck have 1200, 1500, 1800? That should include the weight of people in the cab, cargo in the bed, and trailer TW. Check your driver's door for a sticker that says the max combined weight of occupants and cargo shall not exceed xxxx pounds.