My PB Pellet grill (I think it is an older 340) has huge swings, or what I thought was huge swings. I don't have the lid thermometer (again and older model). But sometimes my digital would be set to 225 and read 400. Then jump to 325. Then jump to 380 and back to 400 again then back down to 325. All over the place. So I put a probe on the grate (a digital probe) and it said 225 right where the temp was set. Not sure why my PB temp probe was doing that but I cleaned it off and it did the same thing. It doesn't always do it, just sometimes but I have learned not to trust it. My external thermometer comes with a "clip" that goes between the grates so the probe doesn't actually sit on the grate but gives a reading. Like i said, when my pellet grill is set at 225 it will be very close and much closer than the digital board.
Chugod Thermometer on Amazon
As for my new Series 3, it doesn't swing much at all, no more than 10-15 degrees and stays on target much better.
In your case it could just be simple science. Heat rises. The Pit Boss thermometer is right near the grate while the analog/lid thermometer is on top where the heat rises. Perhaps give PB customer service a call, they are very helpful but sometimes you can be on hold 30-45 min. The last 2 times I called I was only on hold for no longer than 10 minutes.