I have a friend with an 97 auto 7.3 who had a similar problem where the truck would stall when in reverse. Seems that it was the torque convertor starting to act up. He was told by a mechanic friend to change out his transmission fluid to synthetic fluid. When he did it, it solved the problem...that was about 4 or more years ago.
Early 99 F350 4X4 CC 7.3 Auto. A.R.E. Topper, bed carpet/bench inserts, Rhino grill guard, AIS w/sleeve, Fuel filler mod, GOS headlight harness, 02-04 Headlights, Rancho HD stabilizer, 06 Telescoping/heated mirrors with C-Btr Mirrors, Hella FF1000, Htr Bypass valve, front receiver hitch, Quadzilla XZT gauges, ITP Pre-pump/In-tank mods, Pioneer P5000UB w/XM radio, 4 Infinity Kappa 682.7cf, Fumoto valve, FIAMM Highway blaster horns, SS HPX, IDM mod, DP F5 (Stock,Drive-thru,60T,80E,120,80E-Mountain,1200), Walker BTM, RR, Dieselsite BRV, BTS Tranny, 26 row tranny cooler, Bilstein shocks, Amsoil bypass oil filter, Donaldson ELF7405 oil filter, billet thermostat housing, front & rear parking cameras, Aux reverse lights, Heated Seats.
Security: CrimeGuard Alarm with remote notification, DIY jimmi-jammers, door cylinder locks and linkage removed, padlocked rear bench seat hinge, PCM, DIY "pitstop" switch.