Is there anything I can do to reduce or eliminate the whining noise that occurs while turning?

 

I have heard that it is possible to flush the PS system through the PS cooling system. I have also chosen to use Valvoline Max Life full synthetic ATF fluid to flush the system with.

 

Ford power steering pumps are loud, always have been, some are a bit louder than others, but even new they are loud

Yes, some have had success in quieting a Ford power steering pump using synthetic fluid.

Saginaw power steering pumps are quiet and can be adapted(the bracket) to work on Fords, many with larger tires do this conversion because the ford pumps don't last long with 33" tires, Saginaw's do