I tow a 33RL Silverback with a 2011, F250, 2X4, SRW, 3:75 gear ratio and a 6.2 L gas engine. My trailer is 10600 lb from the factory ad 800-1000 lbs and I’m at 11600, my truck is rated at 12700 so I have some room. If I go to a 4:30 gear ratio my rating goes to 15700.
My payload is rated at 3760 with a pin weight at 2015 lb dry and adding 400 lb for a load I’ll make it 2500 lb. Take 800 lb for two people 35 gal of gas and a 200 lb hitch and you have 460 lb of payload room. All these numbers are fat, I can’t tell you how everyone travels but I want for nothing. By the way an F350 payload rating is 3790 and the same tow ratings.
Also I travel a lot around the Louisville area and I have no problems with the hills there. But if were to go west thru the mountains I would want a diesel, but u already have that. Good luck have fun.