The FICM (fuel injector control module) that was replaced was probably replaced due to the fact that it wasn't producing the proper voltage to fire the injectors. The injectors require 45 volt to fire properly and the DC/DC converter in the modules usually fail. This is a common failure on the 6.0 diesel.
One thing that needs to be done is the computer needs to be programmed with the latest calibration from Ford. The latest calibration has a preheat cycle for the injector spool valves, which will help cold start performance. However if you have one or two injectors that are weak then you will still have the same results when cold. The smoke you are seeing is being produce by the injectors that are not working properly. What will need to be done after you have to computer updated and verify you still have the same concern is a power balance test will need to be performed when the truck is cold and exhibiting the concern. In other words the dealer would need to hook up the scanner and have the power balance test ready to run and as soon as they start the truck the test needs to be started to observe the non contributing injectors. The injector that are not contributing on initial start will most likely be the ones which need replacing.
I actually own a 2005 6.0 with the exact same concern as you are having and performed this test and I now know I need to replace three injectors only I have not come up with the money yet to replace them so I just let it warm up a little longer.
I don't think i will ever purchase a ford desiel again I have had several in the past but this 6.0 has cost at least $6,000.00 to date only 180k