Rough cold start 1999

Please forgive me if this problem has been posted before, but I searched the forum and didn't see anything along the lines of my issue. To start out I bought a used 1999 Grand Prix about six weeks ago w/ 54k miles. It has the 3800 engine. Last Friday morning I got in my car to go to work, started it up, and the engine was running real rough. Not just a little rough, but violently rough. I had to get to work so I drove it there. After a about 5 minutes the engine calmed down and was fine. When I left work, about 9 hrs later, I started it up and it did it again. I brought it home and pulled out my warrenty info. to find where I could bring my car. The local Pontiac dealer accepts my warrenty so I figured it was the best place to bring the car. Anyways after a couple days of running diagnostics they found that each time they ran the diagnostics that a different set of fuel injectors came up bad. They came up w/ a couple solutions. One, they could flush the fuel injectors for $270, but there was no guarantee that would fix it(that was not covered under the warrenty because it wasn't an electrical issue...ppfffttt). Two, they could replace all six fuel injectors for $1500, which may also not fix the problem(again, not covered under the warrenty because it wasn't an electrical failure...double ppffftttt). I called my warrenty company and the guy told me that maybe it was a fuel pressure regulator issue. So I suggested to the dealer that they check the fuel pressure regulator and they said they had. I went to the dealer and the guy said that maybe running the engine would break up the build up on the fuel injectors, so I have it at home now. I haven't tried to cold start it yet. Any help would be greatly appreciated. Thank you.

Damn 1500 for injectors. You can get a set of 42.5 pounds per hour injectors for 280 @ intense,

Did they change the fuel filter??

I know that the store bought injector cleaning stuff isnt real good, but maybe it would be worth a shot.