[gary rabbitt]

Hi,
I am only going to address the trim. If you only 'sand smooth' the flaking areas, then try to spray toner on it, you may end up with uneven color.
Because the light and dark areas will just get darker. Your darks will get darker, and the lights will get darker. So you end up with light and dark places, but both darker that before, if that makes sense.

I'd suggest that the trim areas be taken down to the bare wood. Either carefully using a stripper or better still a 'refinisher'. The second way, which I would only attempt if you have experience, is to use a scraper. Held at the correct angle,(and using a factory made one) , and working carefully, you can remove the flaking finish without harming the wood.
BUT, if you are not careful, you will gouge the wood, or dig in with the corner of a scraper.

For me, a couple of the recent sets I have removed the finish from were scraped. They had flaking finish and it came off just fine. Another benefit is it saves on refinisher or stripper. Of course, when you are done scraping, you should wipe the surface with refinisher to remove anything that still remains.

The thought of scraping a finish sounds harmful but it can be done without damage. If I ever get around to it. I may make a short video on that method.

Just throwing my thoughts about what I'd do to this set.