Hmm the white smoke at startup... is it just condensation? Does it smell like unburnt fuel? (Not sweet smelling like coolant, right?).

I hate recommending things like this, but it is worth trying since they are so easy. I have actually fixed a few cars by:
1) Pull of battery terminal, let the computer do a full reset
2) Throw some fuel system cleaner in a quarter tank

It almost sounds like you have an injector that may be dripping fuel into a cylinder when it is cold/sitting which is causing a stumble until it is burned and blown out. Trying to determine which one would be difficult. I would be inclined to let the truck sit, then on a free morning go and pull the spark plugs and see if you can inspect them visually or by smelling them to see if you can find an outlier. I have had good experiences with sending my injectors out for full service on some older BMW's and Toyotas. Not saying this is your problem, but worth looking into since it is free to at least inspect.