Yes, since making the video below, I have learned that jacking up the front end and turning the wheels lock to lock effectively moves the fluid through the system. How it moves the fluid through the pump with the pump off, I don't exactly know but it does work.
You can use the video to learn how to clean out your reservoir screen and you could certainly run the pump like we did for the fluid flush or do it with the engine off. You're not the first person and you won't be the last that has a shop put in generic power steering fluid when the spec calls for ATF.
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