Floor plan

First things first, did you purchase clear #1 white oak for your floors to start with? If you did not, then do not pursue trying to make another species look like white oak. It never will.

We do have red oak as you have assumed. However, we have seen videos of some Bona products that look like they work.

Bona Red out

Red oak will always retain the salmon tones, no matter how much you try to manipulate it. If having the white oak look is important to you, replace what you have with white oak. Otherwise, clear finish with Bona Traffic, and have a floor that will oulast the bleached white oak trend.

Do you have any pictures of what that looks like?

Getting back to the tile question, would a checkerboard look get old? White/gray.

Something like this but with larger tiles