A year or so back ford released a new software update for the computer. The software (flash update or reflash) actually sends power to the injectors to warm then up (while you are waiting for the glowplugs to warm up) then once you start the truck the injectors are less likely to stick (stiction) and operate normally. The complaint for the flash is a rolling or rough idle, white smoke at start up and hard starting. You appear to have two of those. You may consider spending the $100 or so dollars and have it flashed to the induction flash. It likely will solve you cold running issues. Do a search for "induction flash" to read more. If by chance you are still under the 3/36 warranty it will not cost anything but if not then it will cost 1hr of shop time which is generally ~$100. Good luck.
Member # 23075 Reged: 07/18/02
2005 Excursion w/ 6.0L PSD - Edge Insight, RCD EGR delete, Turbo Drain/Turbo Feed/Blue Spring/Oil Cooler Updates, Dfuser Coolant Filter, 240amp alt, fumoto.
2008 FX4 F250 CCSB w/ 6.4L PSD - Edge Insight, H13 Bi-HIDs, custom coolant filter, "all deleted", fumoto.