I have a 2005 powerstroke. When I bought it(last year), it had 115000 miles on it. After I had given the guy a check, he told me he had run gas in it, but gotten it fixed. I am pretty sure he had run it for several months after getting it fixed.
It ran 7 miles(It started again, but stopped completely after 100 yards). I had been a bit heavy on the throttle. It turns out the fuel pump is hydraulically driven, and the computer won't let it fire if the pressure doesn't get high enough. I had it towed to a dealer, and after 1600 in labor, they replaced some orings in the fuel pump. It required removing the turbo, and a bunch of other stuff. They didn't replace the pump(400$).
It later turned out that they should have replaced the pump. They made it startable by making the computer skip the pressure fault, and the pump failed(in a parking lot, thank God). They had failed to do a thorough diagnostic the first time around, as the fault was detectable. The cost, again, was >2000.
The symptom for both of these incidents was as you described, rough running at initial startup, and no power until the engine was quite warm. The second set of mechanics claimed that half the pump was not firing. The gasoline contamination may have been the trigger, but these engines have a known issue with the fuel pumps that cause these symptoms.
I used to work around diesels a lot, and never had the -lack of power at initial startup- issue. We always let them warm up, but only for ~30 seconds. Power was never an issue.
Good luck.
Chris