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Shinhan Bank & NH Bank should be the most crypto friendly banks, especially Shinhan bank because they’ve also considering a crypto vault service.

South Korea is definitely one of the biggest ones we want to add support for. We're working on finding a service (maybe transferwise) that will allow us to use a large variety of currencies but haven't gotten it all worked out yet. Do you know if foreign companies can start bank accounts in South Korea?

This one, I honestly don’t know. The only thing I know is that banks issue a virtual account to each individual under account holder’s name which then to be used only for that specific crypto exchange, but, it’s pegged to the real bank account the each individual provides to connect to exchanges. This is how the fiat gateway works for major exchanges like upbit, bithmb, korbit, coinone, etc.
But there is this new exchange “Gopax” which doesn’t seem to work this way. This is the only exchange that you can approve/allow withdrawal requests directly from your actual bank account to the exchange so that the exchange can withdraw money out of your bank account to then make deposit to the exchange of your account. And vice versa. Just how paypal works for many other countries. (once you set to allow paypal to make withdrawals paypal will withdraw money from your account when it needs to settle)

I recommend trying out this way for fiat gateway for South Korea.
If you can pull this off, this would be an ultra major break through!!