Like the title says, is there a way to empty out all of the old power steering fluid completely, including the PSC gear box fluid, & replace it with some good Royal Purple Synthetic fluid??

 

Flush it.

Disconnect return hose to the PS reservoir. Usually it's a smaller diameter hose.. Cap/plug the orifice it came from.
Jack the front end of the car up. Turn the steering wheel all the way left/right. This will make fluid **** out of the return hose. Continuously pour fresh fluid into the reservoir to replace the lost dirty fluid. Alternatively, you can fire up the motor, but that'll make fluid **** out really, really fast.