Ignoring the coin jar/charity box confusion, I've tended to keep the bigger coins around and just spend them - a few £1-2 coins don't weigh that much, aren't taking up a great deal of room and will buy your lunch entirely. Then they're not your problem any more.
500 yen's over £3, so I'm guessing you don't get many of those in your lunch change? The top result for "how much is lunch in Japan" [1] suggests that your 500 yen coin would just about cover the next day's lunch and is lighter (barely; 7 grams versus 8.75g) than a British one pound coin [2,3].
The coin sorting machines that you might tip a coin jar into take a decent chunk of your money for the privilege of counting it (e.g. CoinStar charge 9.9% [4]).
1: https://www.withhusbandintow.com/costs-to-eat-in-japan/
2: https://en.wikipedia.org/wiki/One_pound_(British_coin)
3: https://en.wikipedia.org/wiki/500_yen_coin
4: http://www.coinstar.co.uk/FAQ