So if you plug the steering servo into the Spektrum Rx it is twitchy? If so, replace that servo. That could be the culprit. Tap the servo and see if it flips out.
Is your receiver mounted securly? How is it mounted? Check for anything loose that could be vibrating. It could be a wire in the radio system shorting out on something. Try disconnecting the steering servo and test run the car on a stand, tires off. Does it still do it? If so, plug the steering...