The usual way to rejuvenating this piece would have been to remove the bronze gallery , strip the lacquer, and french polish again.
Since the whole house decor was more of a modern clean almost nihilistic look ( Ralf Lauren…? ), the owner wanted a uniform white effect. She sanded the wood with microfiber and applied some white shellac based primer from Zinsser. This primer could grip the possible wax, grease and other residue the wood might have accumulated over the ages. This could be done with a very high quality paint brush.
I then suggested to apply three coats of spray white lacquer, with light scuffing in-betwewen ( 220 grit ).
The finishing sanding would go 600 and 800 grit with water sanding medium. A good coat of wax would really make everything shine. like marble.
The gallery will age. I am sure the bronze will not retain the paint like the wood. Over time, this natural aging will look a very classy chaby-chic!