Typically a temp swing for a 350 setting would be about 15 degrees low and 15 degrees high for a 30 degree swing (low 335 to high 365). Some ovens will hold tighter temps but a 100 degree swing is not ordinary for a fully heated and settled oven. By the way I never check oven temps unless the oven has been on for at least 30 minutes. This allows the oven to settle and balance it's temps.

How long of a time-span did he monitor the temperature? How many on/off cycles of the element (or gas burner)?

The type of thermometer used for testing and where the probe is placed has an effect. Near an element or the burner flume will register a wider swing on heat cycles.

My Jenn-Air is roughly the same. Maybe +- 40 degree swings. Measured with this in the center of the oven on bake convection http://www.thermoworks.com/THS-113-041

He was there about an hour and tested 3 cycles before adjusting and 1 cycle after adjusting. He had the probe wrapped in tin foil and resting on middle rack. Rob m how do you cook like that? My cookies were a mess. 6 batches: some dry and cracked and in there about twice stated cook time, some burned on bottom and raw inside, some generally undercooked...about 2 batches edible with constant watching and readjusting temp once it dropped too low (260).

That's really bad! Old timey ovens were pretty standardly +/- 25° F, which was a 50° span. The compensation for that was to heat the oven for an hour past the preheat time to have the whole oven hot, not just the air. That might work for you, some, but 300-400° is unacceptable, and if Jenn-Air tells you it's normal, I would tell them to take it back. They make "precision ovens" at the ultra high end nowadays that are supposed to vary no more than about three degrees up or down. A high mid-range oven like yours should at least be able to do the old standard for gas!