I'm not too sure you will be satisfied with a 1000W heater, I think the new MES units are around 8 cu ft and they use a 1200w heater and you have about 60% more volume than they do.
Another thing to consider, and I'm by no means an expert on PIDs, but from what I understand from the directions I received with mine and how it functions, is the amount of time you program for the unit to heat up is not continuous, lets say I program the PID to heat from ambient (80°) to 120° in 15 minutes, the PID does not turn on the element and continue to heat until 120° is reached, ...let's say it reaches 120° in 10 minutes and then holds at 120° for 5 minutes, but rather it divides the difference in temp by the time and heats in short increments, I have found that when my GOSM is full and the set temp was not reached in the time I set, the PID holds at that step and does not advance, it does not continue to heat the element.
What could happen with your 1000W element is you will have to set the time for a long period before the target temp is reached.
What I think is the answer when using a PID controller to heat a smoker is to use a high wattage heater 1500W-2000W range, that way when the PID is heating the element is at max and then the target time could be shorter.
Like I said I'm not an expert, I sure wish someone here that is would speak up and help us out and correct me if I'm wrong.