Gus, this is probably a dumb question, but it's not specifically clear in your previous comments. When you had the PID attached, was the analog temp knob set to 250? This has been overlooked in the past. Also, I would suggest putting a good heat sink in the smoker (a few bricks or pan of sand, and a water pan), no wood, no PID, and check the internal temp again. Clip your thermometer probe to the little shelf that the OEM thermocouple is attached to, so it will read as close as possible to the stock sensor, then set the analog dial to 250. I think it would be worth eliminating the possibility of an issue with your particular PID. See if the smoker functions properly, as it came from the factory, then test further with the PID. I'm sure that's a great PID, but so far as I know, it has never been used on this brand of smoker. You definitely sound like you have a very good working knowledge of PIDs, but it seems we need to remove it from the equation to test the smoker.
I have a model 1 that has seldom been idle for very long, and I have never experienced problems with it not getting up to temp, even 250. You are, of course, limited by Q real estate in the #1, so it's really hard to "overload" it, like these guys with a #3.
I only use the #1 in analog mode.