With a PID controller cycling the element faster, potentially as fast as a few seconds, after stable temperature is reached, the element itself doesn't get as cold, and more importantly its peak temperature does not get as hot, as with a thermostat type control with it's much longer cycle time. This means that the peak temperature that the chip are being exposed to is lower, so they don't smolder and smoke as much (or potentially at all.)
Perhaps, one way to combat this would be to increase the cycle time of the PID, if that option is available on your PID (it is in REX-100 style controllers.) Maybe a couple of minutes, such that if the power required to keep chamber temperature is 50%, the element would be on for a full minute, allowing the element to get pretty warm indeed. I have not tried this personally, because...
I am a firm believer in separate temperature and smoke control in my electric smokers. This is an innate feature of my Bradley, and I have added the cold smoker attachment to my MES 30 to achieve this. The chamber temperatures for both are under PID control, and the smoke generators operate independently of this.
That said, the advice to make a mailbox type mod (or smoke tube or maze) is good advice. If the aluminum mailbox (from Gilbralter, IIRC) was still available, I would have done that instead of ponying up for the cold smoker for the MES.