Either put an island back to cover the damage or refinish the floors - all of them- to match. What other option would you entertain? Rug? No one will spot refinish a spot like that as it will never ever match.

Kitchen runner...perfect. Do ruggable, as the backing will keep the rug in place. There are a lot of colors from which to choose.

Am assuming this will be your kitchen. It's not usual but could you place a rug over the unrefinished patches?

You can, just spot fix it and live with the mismatch.

Is there any refinished wood in a closet or other less-conspicuous spot that could be covered by a rug? Under the refrigerator or stove? Or take the wood from the foyer and use a different flooring there?

You can refinish each individual board affected. Just be aware and willing to accept that it may still not be a perfect match.

No contractor wants to be on the hook for a mis-match spot fix and not get paid for a job. We know it's a setup for failure, if, the expectation is for a perfect match. That's why it is best to recommend to redo the entire floors, when there is stain involved., especially custom stain colors.

Why do you not want an island maybe that is where this should start. Show us the new layout and maybe you culd get some matching floor from another space maybe a closet or an entry we have vry little info.

Replace the floor that will be in the kitchen to compliment the remaining wood floor OR redo the whole floor so it all matches OR let someone attempt to match it with the intent that if it does not work you will go onto plan B or C.

Lucky for you. Grey flooring is no longer in fashion. That means you can refinish everything in a pale natural tone and be current.