I have the same problem when it is the first start of the day. Mine is a 2006 with 78,000 miles. Mine cranks about 3-4 seconds before it finally starts. This symptom just started 5 months ago. The truck keeps starting, but, I feel like I'm pressing my luck letting it go this long before fixing it.
Sorry I don't have a definite answer for you. However, I have heard people suggest that the STC fitting could be leaking, however, I haven't gotten around to checking mine. They call this the Snap To Connect fitting. Supposedly this is common for 2005 and 2006's. I'm either waiting for mine to fail completely, in which case I would send it to a diesel mechanic, or a week of Vacation to do it myself. My body is not what it used to be, or I would attempt it on the weekend. I used to spend most of my weekends doing this or that on my vehicles, back in the days,....well, maybe you know how it goes.
There is a kit available from Bullet Proof Diesel for $58 that replaces the fitting with a much more reliable one. Here's the write-up on the Bullet Proof Diesel kit:
'An Upgrade Kit for the Ford, 6.0L engine, 2005-2007. Allows you to upgrade and replace the defective quick-connect style fitting and replace it with a threaded and o-ring sealed fitting. This is the perfect job to do when you already have the turbo off (such as when replacing the EGR cooler or oil cooler).'
And here's the link to the part:
High Pressure Oil Pump (HPOP) Pressure Fitting Upgrade Kit, 2005-2007
If you do replace your STC fitting, please post an update here. I'll do the same, since my symptom seems exactly like yours.
I just had a 4" stainless turbo back exhaust installed this weekend. It sounds and runs real good, but, it's hitting the bottom of the cab, so, I think this will get fixed first. It seems too loud to me, especially since it quiets down considerably when I hit the brakes fairly firm or take a modest left turn....well, that's another issue though isn't it.