Try "neutralizing" Exhaust hangers.
I have a 06 base w/navi. My car seemed to have a vibration whenever I stepped on the gas esp. below 2000 rpms. It sort of felt like back in High School In my 74 Pontiac when I had an exhaust pipe that was close the the frame, when I would turn corners, the exhaust would touch the frame sending vibrations into the car. Well, i Jacked up my TL, twisted and turned all my exhaust hangers. One in particular seemed to be "pre-loaded", The rubber piece had moved all the way up the rod that holds it and seemed to be stretched. So I moved it down the rod (wasn't easy to do, it was rusted there). This mad a huge difference in the total vibrations and exhaust drone inside the car. It no longer sounds like a garbage truck inside the car.