I have read your post, and I was having the very same problem. This first started September 08, and I called a Ford dealer, and they told me to bring it in and did the following:
SERVICE REAR DIFF ADD 2FRICTION MODIDIERS
1 TA 31 SEALANT - SLIC
2 XL 3 ADDITIVE - OIL
4 XY 75W140 QL OIL REAR AXLE
This happened with the milage at 23737 Told me to drive it for about 100 miles or so, and it should stop vibrating. It DID.
Last week, my truck started vibrating again, so I called the same dealer, and they said it could be the clutch. They would have to use diagonastics to find out.
I did not take it to the same dealer, but I did take it to another Ford Dealer yesterday, they did the diagonistics as I waited, and came back and said I would need the clutch pads, and some other parts to be replaced etc. But did say the clutch itself was o k. and the parts and labor is approximately $ 1000.00
I have not decided to have the dealer do this yet. As I wanted to check around to see if I could find something out more positive.
My truck is the same year as yours (2004 F150 Lariat 5.4 Ltre etc. My milage is 27K. I wish I had a true remedy to our problem, and like you hoping someone sees this post, and could give me a definate answer. I don't want to put up $1000.00 not knowing if this will take care of the problem. I have been to TWO dealers now with two different diagonastics. I just wanted to share my same problem. Best of Luck.