H. mathieu needs help  

I own a beautiful H. Mathieu standing lamp (lyfa) but it needs restoration. I tried to clean the metal shades but run into a problem. The thin layer I tried to remove (wich I thought was grease) was probably a sort protection layer. I think it's a sort of cellulose lacquer.
It was almost impossible to remove and it worked out terribly. (see second photo)
Now I need your advice: should I keep on cleaning and removing the layer. And please tell me how? (thinner?, aceton? (The small parts I removed so far took forever...) Or leave it like this?
Please your advice.