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From my experiences with my own Fords, 12 Mustangs for the most part, many of which rolled right off the lot brand new with that infamous whining. However slight as it was, it was there and all of us Mustang owners just got use to it as one of the characteristics of the car.
Lot's of theories and potential fixes, "Snake Oils" and band-aids out there, but assuming you never let the pump run dry and don't need a new pump, these methods have worked for many of us:
One popular plan of attack is to use a turkey baster to remove some of the existing fluid and add Lucas Power Steering Treatment. I have used this on many of my Fords and this stuff definitely works! It really does quiet down Ford pumps and lasts.
Another method is to swap out the power steering fluid for Motorcraft® ATF Type F.
Many Ford guys swear by this. I have honestly had great luck with the Lucas fluid mentioned above, so I never had to go any further.
Another method is with the car OFF, key ON (so the steering wheel don't lock up), wheels on the GROUND, turn the wheels lock to lock with the power steering cap off and look for bubbles surfacing to the top of the resevoir, once there are no more bubbles, turn the wheel the other way and keep it there, again waiting for any bubbles to surface to the top of the power steering resevoir.
The system was properly bled the same way you described. I worked in a ford/chrysler dealership for a few years too. Along with independent shops. I think I'm going to try the saginaw pump conversion when I get time. I've used the Lucas fluids with good success in the past too. Haven't put any in this one though.