First of all, why are you changing the color? If you just feel like trying something different, then I say it's not worth the effort - because the colors you are considering (similar shades of white) will look pretty much all the same in your lighting conditions - you won't really see the difference.
On the other hand, if you are changing the color because you don't like the existing shade of white, then I have a couple suggestions for you:
1. The yellower whites that you mentioned you like may work just fine, so don't rule them out just because they look wrong against your rug. But to check that, don't hold the paint chips against your rug (because you are not painting the floor
Instead, pin the colors to the walls and see if the wall and rug colors clash or look harmonious. Sometimes, when 2 different shades of the same color are placed at a distance and on different planes, the eye can't see the difference.
2. Why are you limiting yourself to shades of white only? A white/light color will not add light to the room, and oftentimes it's a wrong choice for poorly lit spaces.
Hope this helps,