It will be tough to remove and replace counter tops without damaging the tile backsplash. As far as the floor tile, there is grout paint. I have never used the product but it maybe worth looking into.

You can paint grout with Polyblend grout renew(gray). they have it at HomeDepot. Have cabinets painted a soft white, maybe BM Dove White, go with a white granite with some gray/beige in it to compliment the warmth in the floor and then a gray/beige paint. Update the cabinet hardware. Maybe a glass tile backsplash. That might get you closest to your target without replacing the floor. I have used the Polyblend, it's a great product. Best of luck to you.

Wait until you are ready , do the whole kitchen is my advise to you ,