Don't be surprised if a new starter is not in order. Don't be fooled by a parts store doing a bench test, means thing without doing a load test which most of them cant do. Had the same thing happen on my 99, Bench test was good, but I put a new one on anyhow, started right up. I would stay away from Napa ones too, seem to only last 6 months or so.
Shodo said that he replaced the starter already, and still the same.
2001 F350 XLT 4X4 crew cab, dual rear wheels, long bed, black, 7.3l turbo diesel, automatic transmission, 4.10, shift on the fly, running boards, sliding rear window, 38 gal fuel tank, Odyssey extreme 65-PC1750T batteries, Michelin LTX-MS2 rear tires, Sumitomo Encounter front tires, Shell Rotella Ultra elc, 11,500 gvwr, 20,000 gcwr, 7500 gvw, completely stock, 114,000 miles when purchased, now has 240,000 miles, repairs so far: two starters, batteries, cps, brakes, tires, alternator, ball joints, locking hub, wheel hub, AC compressor, serpentine belt, power steering pump, driver's side window, ignition switch, o-ring, Spectra premium radiator, water pump, fan clutch, fan blades, thermostat, thermostat housing, tensioner. Stolen twice so far, but recovered both times with major damage.
2005 Nomad Rampage toyhauler made by Skyline. 11,500lb gvwr.