Can you describe the nature of the noise?
Is it high pitched howl, a low rumbling or a grinding noise.
Seeing you are talking about grinding noise when the tyres are in full lock:
Have you taken a look at the timing belt and the power steering motor? It will cause noise when worn/ damaged.
If the power steering motor is bad, it will also cause a higher pitched sound during full lock.
Driving a BMW318i with LPG at the moment. Had a 2.0 RAV4.1 1997 3drs 4WD euro model w/ABS dual sunroof blue two tone previously.