Just today, I received a response to my request for additional information, and it is both interesting and promising! Here is the update:

"I doubt very much that the chair belonged to a viscountess who put her coronet of rank over the royal arms. If a royal personage gave an object with his/her arms on it to a retainer or friend, that object would be lovingly preserved as is. To alter it, by putting another coronet above the arms, would ruin the piece. Would you change the hood ornament on a Rolls-Royce? (I suppose some people would - but you get the idea.) However, only royal crowns are "closed" - peers' coronets all have pointy things sticking up along the rim, they do not join together. The crown on your chair is a royal crown, not a peer's coronet.

The letter "S" could be significant. It might be the initial of the first name of an owner. Probably a princess, since I cannot think of any 19th century royal male with a name starting with an S.

One other observation: the arms are the "modern" royal arms, adopted after Victoria became Queen. The difference for her was that she did not inherit the crown of Hanover when she became queen because she was a female; that crown went to her uncle instead, and the arms of Hanover were removed from the English royal arms. Victoria became queen in 1837, so we can surmise, if the chair is authentic, that it must have been made after that date. Judging from the photo, and the artistry of the heraldry, it looks right. The chair could be old, and possibly could have come from a royal property. I would need to do more research to tell you more."

Needless to say, this is good news. I've done a little more research today, and there was a Princess Sophia who died in 1848, which would make the time frame tight. I also wonder if the "S" could be for Sandringham House, the Queen's country retreat.