Bleaching will lighten the wood. If, it is yellow. It will make it less or eliminate it. Having white oak means that you can skip the bleaching process. Nordicseal is a good product for white washing. Since, it is also a sealer, it will block any tannins from bleeding through prevent the yellow. Also, if, you use a water base poly, the water base poly will prevent the yellowing. If, you use an oil base, then expect yellowing to occur. You can also use a stain mixture for white washing. But, you will need to apply a sealer to prevent tannins from bleeding through.

Well said blondelle. I would stay away from gray on red oak. It can be done....but it takes an expensive professional to get it to the level you are looking for. It would be cheaper to spend more money on WHITE oak (as much as $2/sf more) and have it stained gray then try to reverse the reds in red oak to look 'gray'. If it were me, I would look to a lighter stain that has a GREEN base to it. The green will counter act the red to offer a COOL tone brown (like a mushroom brown). Turning red oak to a cool brown is much easier and often gives the homeowner the same CONCEPT (cool toned flooring) without stretching the talent of the flooring professional. And yes, gray as a design concept is at it's end.

Another reason not to mix custom stains. It doesn't take much to make the incorrect mix. Samples are measured with spoons, then you have to figure out the ratio for the actual project. It becomes more difficult when you need to do touch ups or spot fixes, which will most likely result in a entire floor refinish. Make things easy for yourself and stick to standard colors.

You want to avoid applying a second coat of stain. It will cause adhesion issues. What you can do is add some of the stain to a oil base poly, then apply it. Another option is to use poly shade in a similar color. You can apply 2-3 coats of the poly shade to achieve your desired color. Poly shade is oil base. Contractor should have water popped the floor prior to applying the stain. The color would come out darker.