APPS= Accelerator Pedal Position Sensor. If it were that, I think you have driveability issues.
A bad connection can cause weird things. The ECM and/or PCM get information from different sensors, in various places. If any were getting/giving eroneous info, it could have an effect. The programming uses the info and the parameters in the programming to make the neccesarry changes. Whether timing, fueling, or whatever.
Has there been any change (a drop) in mileage, at all? There are some sensors that need to be cleaned up sometimes. IAT (Intake Air Temp) sensor being one.
Could be the injectors need to be tested, if they are original.
My trucks timing is retarded. I get the same colors from the exhaust, same as you.
It can change from differences in boost vs. fueling. Not as much fuel+ lots of air= whiteish/gray smoke, sometimes blueish. Lots of fuel + not as much air= black smoke.
I tend to get gray/white smoke when snapping the throttle in neutral. If I don't lug the engine, and the boost comes up quickly, I also see gray smoke. If I stand on it with little to no boost, it is black as coal. Low cylinder temps with the 370s, in the winter cause white smoke at idle. Even if just coming off the interstate, waiting at a light.
I had the HX-40 installed before the 370s came. Lots of air. Air gray smoke on hard throttle.
Have you disconnected the Power Puck, to see if anything changes? If so, what?