about the paint

I think you should carefully try to clean it, you can wetsand it but not too close to the artwork.
some careful use of rubbing compound also.
the rust is most likely going through the paint under it-wetsanding the rust might show the paint.

raw Linseed oil(not boiled) can be applied-it will brighten up the color.

I bet it will clean up very well

-show us a nice closeup of the wooden rims!