There is something you need to be aware of with these coins, and with handling bulk copper and bronze coins in general. This is the existence of "bronze disease".
Bronze disease, despite it's name, is not actually biological - as I said, copper is poisonous to most molds and fungi. But it is called a "disease" because it is contagious just like a real disease - it can spread across a coin, and can jump from coin to coin, either by direct physical contact or by pieces of dust breaking off a contaminated coin and landing on another coin. You've mentioned a powdery appearance and a "dust" that comes off the coins when disturbed. These are both clear signs that it's bronze disease we're seeing here.
Bronze disease is the formation of copper sesquicarbonate - a complex mixture of carbonates and bicarbonates, along with some copper hydroxides and copper chlorides (if salt was present in the environment). It is powdery in appearance and typically pale greenish-grey in colour.
Bronze disease can be treated to remove the corrosion, but it does require some kind of acidic or chelating chemical. Dumping the coins in a big bucket of acid will destroy the bronze disease, but also destroy the appearance of the coins; there are less drastic treatments (such as Verdi-care) that do the same job without damaging the coin so much.
Bronze disease can also be "killed" in the sense of the spread being halted, by heat - spread the coins out on a baking tray and put them in the oven at around 100-105 deg C (around 220 deg F) for an hour or so. The coins will still look ugly and corroded, but at least they won't get any worse.
A good rule of thumb: NEVER toss ugly green coins into the same box or bucket as perfectly good not-a-speck-of-green coins, just in case there's bronze disease in there and you end up ruining those previously-good coins. Whenever I'm sorting coins, anything with even just a speck of green on it gets tossed into a separate bucket, for dealing with later.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis