You'll be fine using the bumper ball and the trip in general. The bumper is rated for 2k lbs and 200 pounds tongue weight. Keep the rpms up on the hills and the 3.0 will pull them no problem--you'll probably have to use 3rd gear.
I went on a dune trip recently towing a trailer w/2 quads on in (about 2k lbs total) for over 650 miles using the bumper ball w/o a lick of trouble or damage--towed great. Truck also had about 600lbs of gear in the bed and cab. The 3.0 did great, pulled over a dozens grades/hills at 60mph with power to spare. Ran em' 3rd gear at 4k rpm.
Tire pressures sound correct. I think you'll be surprised at how well the truck tows.
99' Ranger XLT 4x4 Ex. Cab. Lowered 2.5"/2" (Removed blocks & 08 Keys) 3.0FFV, 5spd, 3.73's, 245/70-16's on OE Teardrops. Clear corners, 06 Tail Lights, Tinted Windows, Explorer OHC, U/D Crank Pulley, E-Fan, 02 Composite upper, 05' Ranger half-shafted TB, EGR Delete, 06 Mirrors, Sound Deadened w/Raamat.