It sounds like a horse trotting underneath my truck

Lifters?

 

Catylitic convertor heat shield loose or honeycomb stuff loose inside convertor.

 

This would be my guess as well.

 

If it makes it at idle I would get a stethoscope and start probing around underneath the truck...

 

Since you said it's there at idle my idea goes out the window.

For anyone else experiencing weird noises when moving though, I had a doosie tracking down a rattle noise that ended up being the ring inside the center cap of one of my wheels came loose because a tab that held it in place broke. It was just flopping around inside the center cap (or whatever its called).

 

Neigh.

 

The 4 liter has no lifters.
Buckets.