Use "live sawn white oak" with Nordic seal and traffic HD. The nordic seal will give you the white wash. The mineral streaks will give you the gray. HD will provide the proper protection.

If, you match what you have, you will not get the look you want.

Thank you however we were not planning on replacing our stair treads. Just too costly. We need to work with the red oak to try to match to the floors.

Then do the treads in a dark gray since the 2 oaks will take stain much diferently

I agree with Patricia Colwell. White isn't forgiving when attempting to match White and Red Oak. Best to pick two complementary colors.

I suggest you go with a dark stair tread and white risers if you are keeping the red oak treads. I would even look at something as strong as a "black" tread. Match the risers with the "soft" white you are achieving on the floor. That's how you can get everything to tie together.