A "good" colour master will be able to offer an almost perfect match. Personally I would work with a "tone on tone" look. The floor finisher will come in and produce "stain" patches (4-5 different patches on your floor...with stain and a coat of finish). This will be done on raw oak (fully sanded and ready to take a stain). This is the best way to go about it. You will have a few extra days without a finish on your floor, but the colour match will be darn near perfect.

Once the stains are produced, you get to choose which one you like. The professional then comes back, sands down the colour patches and gets to work applying stain over the entire floor.

The DIY colour palette from DIY level finishes (like minwax, etc) won't get you the floor colour you need. You need a professional who has been mixing colours for several years and has experience mixing several colours to produce a unique blend. It is doable. They do this every day all day. If the professional you are working with can't get it done, then you might want to move on (move up the experience ladder to someone who mixes colour x 20 years).

Thank you for your feedback! When you say "tone on tone" what exactly do you mean? Is that the mixing you are referring too or something different?