Factory radio system is AM. That's most of your problem.

I can only gather that the interference wasn't strong enough because the NiMH cells can't produce much current. The LiPo allows the motor/ESC to draw much larger pulses of current which reach out farther from the wires and interfere with the AM radio signal. It happens especially on acceleration because that's when the motor draws the most current. Am I right BrianG?

You could try to relcate the reciever as far away from the motor/ESC as possible. Try putting it behind the front bumper just for kicks. If it doesnt help then you may consider wrapping the motor/battery leads with aluminum foil to help shield the reciever. If neither one helps then I think you need to upgrade the radio system. Either FM, PCM, or 2.4GhZ (DSM) will be pretty much immune to this type of interference.