More likely the U-Joints. Very typical of U-Joints to make noise and/or vibrate under load and then the problem goes away when you let off the gas and take the load off the U-Joint.
It's always best to just replace both if one goes out. U-Joints are fairly cheap, and only requires about 15 minutes more more labor to replace the other U-Joint, once you get the drive shaft out of the car
I would agree with Richard. I have had U-Joints fail, and this is an early symptom. Dealer replaced the entire rear driveshaft of my '10 Limited under warranty because replacement U-Joint did not eliminate all the vibration and rumble. New driveshaft fixed it fine.
Gavin is correct that some early model Gen-1 Sport Trac's had a problem with vibrations at higher speeds(70 mph+, not 35 mph) that was caused by the steel drive shafts. Ford replaced many of those drive shafts under warranty with new aluminum shafts....that seems to have solved the problem.
I really appreciate all the help Rich, Eddy and Gavin. I am in afghanistan doing a tour with my MN Army National Guard unit. I have purchased some nice things for a ST that I have waiting for me at home. I love this site and will be posting LOTS of pictures when I get home. I have some fun Projects in mind for the ST. Thanks again!