Every conservation effort is different and depends on the damage. While oil paints on copper may not face the common problems of broken canvases or deformed wood panels, they do have their own unique challenges. The real question is how valuable is your painting to you? If, for example, it was painted by a special relative, it can have great sentimental value, both for you and for anyone you want to bequeath it to. If you are unsure of your real market value, we can probably provide you with a general estimate or point you to potential specialists who can provide you with a more accurate assessment.
In general, we don't consider the value of a painting when we commission it, but we start from the premise that our goal is to achieve the best quality of work for each work we do. Before oil paints can be repaired, cleaned or removed from varnish, they must be evaluated by the curator. A typical oil painting can have a variety of unique pigments or varnishes, all of which require testing on a patch to see what type of solution should be created for cleaning. The types of paint in a historic work often include unusual pigments, such as Egyptian brown (made from Egyptian mummies), lapis lazuli (crushed gemstones), white lead, and even shades of green that contain levels of arsenic.
After reading your article, I'm concerned about insurance in case the paint gets damaged or I damage the paint. While a family portrait or a prized ornament can be restored for personal or historical reasons, an oil painting or sculpture can be restored to maintain and preserve a financial asset, or add value when auctioned or put up for sale. As long as the damage does not materially affect the original work, they can restore the painting without diminishing its value.