I didn't listen to the videos yet but I will almost put money on a heat shield or cat rattling on the inside. It's happened to every one of our F150s. I did have one making a bad noise once and it ended up being one of the lift brackets mounted on the heads. I was vibrating at idle. With the engine running take you hand and grab the lifting brackets and it should stop. If not, when the truck is off and cooled down take your hand and smack the exhaust up next to the cats in different places and on the heat shields. You have something that has come loose and making the noise.
