Diesel Bombers - Barely running after idling for 20 minutes

Hi guys
I'm new to the forums but have been lurking. I've got a problem that I'm hoping some of you can shed some light on. I'll preface this by I know absolutely jack about the 6.4L. I've got my cummins figured out pretty well but these Fords are new to me. I'm in charge of our ambulance maintenance, I'm sure the problem I'm going to describe is way above my know how or pay grade but I would at least like to know what could be going on.

This morning , like 0030, I was on a 911 call in our 2010 F350. Went inside, did our thing, and when we came outside, the ambulance for a lack of a better term, was running like s***. It was running really rough, wouldn't go above 1800rpm. When the engine got above about 1000rpm it had a really bad miss to it. My partner shut it off, started it back up and it ran fine. No CEL or wrench light. About 20 minutes later after driving it 25 miles like I stole it, we had to let it idle again. Came back out of the house, running like crap. Repeated the off and on. Took about 30 seconds and it did the same thing. Shut off, start. This time the CEL was on. Got to the hospital, dropped off, plugged in a code reader I had in my bag. (dont know why i had it in there) PO306.
It's running fine now, but I'm just wondering what it is or might be? I have nightmares about our 08 that started missing and them ate the HPFP. Any help or direction would be greatly appreciated.
Nick