This would probably work for you :

Here is a link that might be useful: Smooth On site

Thank you for the idea, ingeorgia. I will need to make several small pieces, I think, shaped with my fingers and small tools. I'll investigate this option more to see whether it would work.

That sounds like neat stuff if you can find it. If not, I would think that most filler would work; you can get wood fillers in wood colour too. Or, if you want to make the pieces off the chairs and then glue them on, maybe polymer clay?

Are there intact carvings that you can make a mold from?

You're pretty intrepid to take this on!

Karin L

Thank you very much for the ideas, Karin.

We ended up finding a different solution. Each of the two chairs had a different area of damage to the embellishments. We removed an embellishment from one chair and cut it (with a utility knife) to get the missing piece to drop into the other one. It worked nicely. These are really pretty chairs, but I think the seller was intentionally tricky in her listing. But now repaired with glue and tightened up, oiled, seat reupholstered and with the detail restored, we now have one great chair. We haven't decided yet what to do with the other one, which is a matching but very small and low rocker.

Thanks to both of you for your input!

I would make a silicone mold of the pieces you need, taken from the opposite side of the design The product can be bought at Michaels or any craft store. When the mold has solidified, you would use plaster or a resin or replicate what you need.

You might need to do a little sanding to get the right size, but all in all, using a mold would be much easier than trying to free-hand the design.

Here's a video that might be useful.

Here is a link that might be useful: video

Another product that's got good reviews/results and would work for both large and small jobs is Abatron. I'll add the link.
Best of luck,
Ging

Here is a link that might be useful: Abatron website