I guess my last post didn't get up there. After I changed the alternator it didn't get any change at all. $250 plus $60 diagnostics didn't change anything

 

Moose, That's a stinker! I'm certain that frustrated you to no end, it would me. I said earlier that I'd heard of interference caused by the alternator going bad. One of my trucks had that issue and the tech(Old school guy that I trusted) chewed my rear for not replacing it with motorcraft( I used an aftermarket rebuilder to save some bucks) His point was it's a known issue and while the aftermarket Alt put out a charge, I couldn't insure that it didn't contribute to interference. I think I wound up having him replace the aftermarket with a rebuilt Motorcraft but can't remember the outcome, sorry.
Not sure that's the answer to your issue, just relaying my experience to you. I'd go back to the simplest of diagnostics; plugs, COP's, injectors. I had a cyl 6 misfire and a random in my 5.4 3v for a long time that I couldn't get a handle on. See my post titled "PO306,PO300 miss that wont go away" I'm not smart enough to provide you the link w/o researching how to post it here. Point is I thought I cured it with a new motorcraft plug and existing motorcraft COP. Turns out my diag for insuring a good COP was flawed, using my ohm meter I checked resistance on number 6 and compared it to others, all were around 5.5 ohms so I thought the coil was good. In actuality the darn COP was bad on #6, it would ohm fine when it was cold but would fail under warm/hot conditions.
I was ready to set fire to the truck after about the second or third time I had to pull COP and plug out of it! Further I was sold on the idea that the timing was screwed and was contemplating replacing all that. In the end it was something simple and I hope yours is also.

 

Here's the latest news. I just had the dealer replace the cam phasers for $1200. They told me it was running perfect. I pay and jump in my truck and its running exactly the same. I grabbed the shop manager and took him for a ride and he agreed the problem isn't any better. Ugh!