OK - I have the blue/gray smoke/haze again.
About three months ago I had this problem, it's not as bad right now. I pulled the injectors back then and found them to be coked up pretty bad - cleaned them up and all was fine again.

The smoke began again shorly after adding used motor oil to the tank - only 1 gallon per full tank. Could be coincidental, but either way, no more used oil. Could it be causing the coking of the injectors? Assuming they're bad again.

I'm sure the valves also need adjusting.

Three Questions:
If the valves are in need of adjusting, is blue/gray smoke a sympton?

Rotating the motor - I think most recommend using the alternator to turn, when I tried this the pulley just spun within the belt.
I picked up a new GatorBack to change the belt.
If the new belt does not work, how best to rotate the motor? Barring tool? Any other ways without the barring tool?

If I pull the injectors, I'd imagine a shotgun bore swab would be best for cleaning the bores - any other suggestions?

 

You can also rotate the engine by using the bolts on the dampner, I think they are 15mm? Kinda hard to do from up top though. Don't know that valves would cause the haze, but couldn't hurt to make sure they're right.

I know there is a link around here to the step-by-step on your valves. Just do a search for adjusting valves.

 

I would think if you run used oil or any kind of oil in the fuel its going to smoke more. Gray maybe whitish smoke could be pluged air filter.

 

Each tank I run 3 times the oil you ran through yours and havnt had a problem yet. I pulled the original injectors with 230k miles on them and they had deposits on them but far from clogging the tip. I would say less than 25% to the exposed tip had deposits and most of it was more of a varnish than clumps. I would also recomend checking in another place.
You list your truck as stock. The only other place I can think that may lead to deposits and smoke is if you dont have enough turbo boost. My truck only hazes at idle before the motor warms up. After boost builds (a couple PSI) the haze is gone.
I would suggest buying a barring tool from cummins. They are less than $35 bucks and worth every penny in the form of less agrevation. If you dont go that route then the alt pulley and balancer bolts are about the only way to bump the motor over. I couldnt use the alt nut myself do to a weak tensioner.
Timing should help clean up your smoke also. I didnt bump my timing to after I swapped fuel plates but it really helped. I run just over 16 degrees and gained MPG, less smoke, and lower EGTs. Definatly worth doing.
For the injectors use a short chunk of 3/4 inch EMT electrical conduit and a lug nut to pull the injector. I bought a wire brush like a shotgun bore brush in the plumbing department and used that with great success.
You didnt ask but I would suggest installing a 3k gov springs in the Inj pump. They really make these trucks alot more fun to drive.