Never woulda guessed a pink shift with this one -- it's way deep in the Yellow Hue Family closer to Green-Yellow than Yellow-Red. If it were anywhere near YR, the pink would make sense.

Do you have a rug? Colors?

I wonder since changing lighting didn't work if you could shift it by adding a large element like a rug with reds. Red because of CC's hue family. I'll spare you the pedantic color theory details.

Just buy it from somewhere that you can return it if it doesn't work.

I am not completely surprised that it is pulling pink/lilac. I see a bit of it when I look at the sample and I know that really low chroma values can mess with our perception of color.

Here is another person who sees the pink/lilac undertones. . .

https://thecolorconcierge.com/cloud-cover-color-review/#:~:text=Benjamin%20Moore%20Cloud%20Cover%20(OC,off%2Dwhite%20on%20your%20walls.&text=It%20looks%20great%20in%20a%20room%20with%20north%20facing%20light.

I would test Cloud White.

Here is a quick compare against the hickory flooring. Cloud white on top Cloud cover below.

Cloud white will still appear white, but has just enough color to keep it from shifting.

can you post pictures of your floor? I am leaning towards Roswell Hickory but am unsure if I like the knotty pattern