I heard someone say that the payment machines in 7/11 can work as a coin processor and give you bills back. I've never tried it though.
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Do you still have a bank account? You can deposit about 100 coins into the ATM at once. Usually only the ATMs in a branch will accept coins. These days, most banks will charge you for more than that.
Also, if you put too many coins into the self registers, they will return bills as change.
But yeah, these days there is no quick and easy way to do it if you have 2kg as you say.
You could also use it to charge Suica, but the machines don’t accept the smaller coins.
I’ve never had the problem you’re experiencing to be honest. I use electronic money almost exclusively these days, and when I get coins I use them as I go.
Anyway, good luck!