4000 pounds is a lot or weight for these trucks (250 & 350 SRW's) when travelling 120 miles round trip. That weight will exceed the tire ratings (axles too), even if "E" rated tires are used. I have "F" rated tires and 4500 lb rated wheels and have hauled that weight a short distance. I wouldn't want to haul it on the highway that far. You should consider splitting the load wth your trailer. Stopping that load while in your truck bed could be an adventure.

BTW your truck probably weighs 7400+ lbs and is rated to carry a GVW of 8800 lbs. (at least legally, provided it is a 2004 or older F250). If you do the math, even 1 ton is past your legal limit.