The Cu-Ni coins can be salvaged. Rub them lightly with a very soft cloth (I like to use old baby clothes).
If this is not enough, cover the coin with a thin layer of baking soda (sodium bicarbonate). Sprinkle the soda (not the coin directly!) with a few drops of citric acid. The two will react, foaming and fizzing. When the reaction has finished, neutralise with warm water. Dry well (same baby cloth, followed by a bask in a warm place, e.g. a central heating element). I got this recipe from legendary Amsterdam coin dealer Jacques Schulman, who said it can be used on proofs. I used it on unc coins only, though, so you are on your own for proofs.
The bronzes are more iffy. Try the baby cloth first. If necessary, dip it in some acetone. Important: do not use Schulman's recipe on bronzes.
If it's any comfort, paper would likely have had the same effect. Try keeping them proofs in a plastic coin cabinet with covered drawers. Check regularly. Repeat the above when necessary.
Peter