Gladly. Unfortunately, I have to preface that I would never start it for us. The risk of ruining the window sills would be too great for me, and creating an even raw surface would take too much time.
Polished is smooth and does not necessarily absorb evenly; water will definitely gather on it. You could sand it with a fine grit, but you can't reach the corners perfectly.
Sealed is often "plastic." Where, for example, a thin film (acrylate in aqueous solution) has coated the particles, a reaction like silicification is no longer possible. You really wouldn't need to bother anymore.
The sample area provides clarity. But is it worth it? If I were restoring a treasure, I would consider a partial change so that the color temperature matches. That is usually enough. Maybe I would also just avoid letting hard white near it: something warm-toned only really stands out when you contrast it with something cold, i.e., if there were a clay wall next to it, you would perceive the room as warmer with the cold window sills than with warm tones. Too much harmony is dull and cannot enhance the desired effect.