I agree with CP, your snubber definetly needs more room than 1/2" of travel. In a normal drive down the street, you are going to need more travel than that, so I'd bet it is bottoming out. Try removing it and see if that improves the ride. It is only a few bolts to take it off.
Similarly, I bet your have inadequate travel in the front as well. You didn't say what size your torsion bars are (they are the springs that hold the front end up) but with teh stock sway bar and stock style shocks, I doubt our t-bars are oversized and they are probably stock as well, ie, they should ride pretty softly, so I suspect you are bottoming them out.
Mopar ride height is not measured at the fender lips. Up front, it is measured on the lower control arm. Odds are it is not stock height at all. When set to factory specs, many Challengers appear to be nose high. If yours is level, it would tend to suggest the nose has been dropped. If your rear springs are original, they are probably worn, whch reduces height, which means if the front was lowered, it is way beyond where it should be for travel. Look at the space between the lower control arm bumper and the frame. This should be very telling. If its an inch or less, or if the bumper is fragged, you don't have enough travel. The good news is you can gain this back pretty easily be turning up the t-bar, but if your overall ride height changes more than 1-.5", then you will also need a new alignment.
FWIW, to find the ride height you are at, you want your car on a level surface. Measure from the floor to the t-bar socket. This is "A". Now measure from the floor to the lower ball joint. This is "B". Subtract B from A, this is your ride height. Measurement A should be 1 7/8" higher than measurement B for a stock ride height. Most guys tend to lwoer their cars down a little bit, but if yu go too far, then you run into inadequate travel that creates this tye of problem.
measurement demo below
