An indictor of a PS pump whine is its either resisting (ps pulley bearing) or too loose (air inside the system) causing inconsistent pressure during full lock when the rack’s tie rods are fully extended and/or drive belt is slipping. How is your drive belt and when was the last time it was...
Your method of bleeding the air out is correct.
Is whine still present even when the wheels are up?
What power steering fluid are you using?
Are there any sediments at the bottom of the reservoir after 2 flush and fills (flashlight)?