We are installing a QS red oak floor and QS white oak cabinets. I guess we are doing the opposite of what you are proposing... The floors will just be sealed with no stain and the cabinets will have Miniwax red oak stain. We wanted the wood to complement each other but definitely be distinct so they didn't "blend into" each other.

Try anything you decide on a piece of similar wood first---it is difficult to remove stains. Yes, you can do what you suggested. Sanding will need to be done after each step---except the last one. However, as most woodworkers find, finishing properly can be more work than building the project. A good finish needs proper preparation(oak does not take much), proper application of stain/colorants(again, fairly simple with oak---especially if the stain is hand applied with a rag/brush) and correct application of final finish(follow the manufacturer's instructions with NO short cuts!)

I like White Oak better than Red. It works better with a certain color pallette and is less grainy when stained. I have natural color White Oak in my master bedroom. Traditionally flooring here was White Oak when stained, Red Oak when natural, but that's going quite a long way back. Two things to consider. 1) The floor in the pictures looks almost certain to be #1 Common grade. White Oak will have some substantial color variations, especially in a grade lower than Select. 2) $1.00 per square foot additional for staining sounds like a lot. We charge $0.30 per square foot to go from natural to a standard stain. It takes a bit more time to make sure you've sanded out the small scratches that typically wouldn't show up on a natural floor, but you're not adding an extra coat. You're simply applying stain instead of clear for the first coat. I could see if it was a small area and might require lots of samples but not 2000'. Maybe he's charging for the stain as a separate added operation and still applying the same number of surface coats. Or possibly he uses a better (ie more costly) crew to do the stain jobs. Or maybe I'm not charging enough!

Like jfcwood states - the FINAL colour is the true test as to whether the experiment "worked". The other problem contractors have would be the use of oil based or oil modified finishes. It is impossible to get a white floor when the top coats turn ORANGE! I once had a "professional" (15 years in the refinishing business) tell me he worked with "water based" finishes all the time. He then named every SINGLE oil based product on his shelf. It turns out he thought that anything that was liquid - like water - was water based. He couldn't name a water based finish if it jumped up and slapped him with a lawsuit! The "old guard" are having a hard time adjusting to the "new" thinking. The Low VOC stuff, the 'non ambering' stuff, the low-odour products are relatively new (to North America...they are de rigueur in Europe) and are different to use. They require training. Training is no big deal in Europe. You have to do it to keep your license. North America is still the wild-wild west. If you have a sanding machine, you can call yourself a floor refinisher (sad...but true). Add that to the fact that red oak is cheaper than white oak and the trend is white flooring, you get a powerful mixture of fashion together with lack of knowledge and a healthy dose of "cheaper is better". A whole bunch of hearts have and will continue to be broken - on both sides of the professional-client fence. My advice: If you want the look of European Oak, then you should start with European Oak. If you are lucky enough to like the reddish tones of Red Oak, then go ahead and work with Red Oak; count your blessings and the money left in your bank account.