The timing does sound like the steering lock on your Limited. You should be able to hear that even when it is not screeching, so that you could compare the timing of the sounds.
Try turning the steering wheel, particularly if you are parked on a slope, to take the pressure off of the lock before starting. The steering lock will limit the wheel travel before you start. So if you could feel out that range of travel, and put the wheel midway between the limits, that could ease pressure on the locking mechanism.
2009 V6 4wd Base