You might want to see if you can find someone with the software program named AutoEnginuity and hopefully they will have the full Ford module or it might pay to buy it. I have the same engine as you and noted a strange stumbling after I bought the truck in 2004 and it was fuel pressure related. The software can run and record what is happening with injectors and any other settings and I had a fuel filter that was needing replacement. I do it once a year now and have had no issues since. I did add an aftermarket Edge tunner, 4 inch exhaust and free flow intake system and when I tow anything I bump up the computer to "race" setting and found I only need 2/3 of the throttle I used to need.
If the turbo was failing it generally will start burning oil due to failing seals so hopefully there is no oil smoke or loss of oil? You should not even feel a 3500 pound trailer as I pull a 36 foot 5th wheel and when it had the race car in it was about 12,000 fully loaded and it still got 14 MPG. I have had a couple of occasions where I had bad diesel and it could be that so did you fill up recently at a new diesel source?
Another item is to check all the connectors to see if the dealer left one loose on purpose to help you want to get rid of the truck.
The final thing it could be is the ICP sensor and see if the connector is full of oil and if so it is failing. I carry a spare as they can fail for no reason and even Ford has had batches of bad ones.
Ford Powerstroke Forum is the place.