You will likely never reach your goal because you are starting from two diffent points. Red Oak will never look like Ash because it will ALWAYS HAVE A RED BASE. Additionally, there are all different grades of wood flooring that contribute to the final color appearance.

Try various stains on your floor and see what works best for you.

I would try Duraseal Chestnut with some White and a bit of Neutral. If might be a bit more red but it should have that nice nutty brown color.

But couldn't you first apply Bona Red Out to remove the red from the red oak floor and then apply a stain?

(Why do you want a gray floors which are so inconsistent with the interior doors and railings shown in the photos?)

The Red Out might help, but if it causes grain-raise the floor should be lightly abraded between the Red Out and stain application.

@wdccruise my floor guy doesn't work with the Red Out. I used it previously and didn't see much difference. Also didn't even notice the banisters/railings/doors until you said something... I was so fixated on the floor color. Agreed if this were my house those things would be changed.