Re-reading the Op made me think.
Put the Engine on the track, apply a low voltage and wait.
Does the engine wait, then start off slow or Jerk into motion?
If it waits then starts slow it's just the delay they put into it.
If it still jerks to a low speed it is something else.
Perhaps handling the engine is making the side rods bind, then once they free up it's OK.
Stop it and let it sit without touching it for an hour, Try again.
If it jerks again you have a problem.
If it doesn't jerk the second time run it slowly and observe the side rods for binding.
First, look for a bent rod hitting something.
Then check to see if a screw on the drivers is backing out and hitting the rods.
If no help there:
Open the engine and rotate the flywheel on top of the motor (assuming it has one) and see if it rotates smoothly for many turns. Make sure you rotate enough to make the drive wheels go all the way around once or more.
If it jerks or binds back off and go again, see if it hits in the same place.
First, check to see if something is hitting the Drive Rods.
Then try removing the screws from both rods on a set of wheels.
If no change put those screws back and pull the screws from the next pair of wheels.
While the screws are out look for flash or rough edges on the holes for the screws. I've had trouble there on other engines..
If it still binds, Pull the motor from the truck and inspect the gears for a rough spot.
Check each gear carefully, it can be hard to spot or it can show right up.
I'd doubt this one as you say it runs good after one jump start.
It may be that the Grease needs replaced in the gear wells.
Older grease can set up but it usually takes years.
Once it is open I would replace the grease with Red N Tacky #2.