My 00 5.4 is doing the same thing! She stutters/misses when you start start to accelerate, and then once you are moving it doesn't seem as bad. Then once it shifts into a higher gear you can still kind of feel it there when you place her under load again. No codes or blinking cel.
I just replaced the fuel filter, got seafoam in the tank and I ran some through the brake booster intake. It's not missing as bad, but it's still there. So I think mine was a combination of a couple things.
I'm going to grab some cops and motorcraft plugs too.
They don't look like fun to change though lol