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late build 03 f350 auto,i got a p0500 code and noticed sometimes after 2rd-3rd gear engages theres a shudder or fast vibration for few secs unless i let off,it didnt start this till i took batts out, where is the location of the vss at,im seeing some say at each wheel,ontop rear diff,ontop back of trans so not real sure?
The sensor at the rear differential feeds the abs, then it goes to all other electronics; pcm, gauge panel, cruise, OH display. I believe the trans takes its clue from the pcm. Are any other components getting the speed signal? Gauge? ABS light on?
When i use the tow haul noshuddering at all, for a day my tow haul would blink,discon batts,drove awhile and feel shudder insome gears,cked with forscan p0500,its a 4wd if that matters,i cked all fuses,all good.
If the ABS light was on too, then there may not be a clear signal pattern out of the Speed sensor in the rear diff. You could try pulling it and see if it's covered with metal wear particles. If so, wipe them off and see if it improves. In the future you may still need to replace the sensor, but check if it's wires in the area are damaged.
I'm not sure how sensitive the trans software is, if a varying signal will interfere with the shifting. But for trans issues Mark K is the best person who would know.