Sound travels funny. It may sound like the rear but be the front so don't rule out that the problem might be up front. How is the ride? I've never driven a car with bad shocks so I can't say how the ride or handling would be, but as low as the LS sits, and the way I've seen tires on cars with bad shocks bounce, I could see a bad shock letting a tire bounce off the inside of the wheel well making a noise like that. To check the shocks, you push down hard on a corner, and the car should go down, come up once, then settle. If it goes up and down more than once after you let off, that shock is bad.
This should have been found when the tires were changed, but a prank people sometimes pull is to take a large zip tie and tie it to the driveshaft. When you drive, the end of the zip tie will slap the bottom of the car, convincing people that they have a problem. It too will change according to vehicle speed and not RPM.
