Well, I'll go back to my first thoughts that something is vibrating when the engine is under load that is causing that vibration sound.
What I would do is to take my car up to the local automotive shop and request the oldest mechanic they have to take a ride with me and let him hear the noise.
Then suggest he put it on a rack and pound around the undercover panels with a rubber mallet to see if he can duplicate the noise. If not, take off the front under panel and bang around the exhaust heat shield with the rubber mallet ..... then do the same with the rest of the exhaust system.
Betcha he can find out what is making the sound ......... then take a crowbar to that piece and push it over.
WOW! ....... how hi tech ........
humfrz