I recently just sent 6 million won home (exchange rate is the best it's been in the 6 years I've been here!) at Daegu Bank (I actually send about 1 million home a month, normally)
It gets wired to my TD Canadatrust account, cost me 15,000 won on this end to do the transfer + I think 10 or 15 bucks on the other end.
You'll need your Alien Card & your home bank details (bank address, swift number, account number, bank name and branch number),
-and either cash or your korean bank card. (for the first time).
I've never had to show my passport, or any immigration-related documents
After the first time, you just roll into the bank with your alien card and everything is on file (bring last transfer receipt for any language breakdowns)
I've never had any problems, questions asked etc about sending money home. Mind you the most I've sent at one time is around 6 to 7 million. Perhaps breaking it down into smaller chunks will save you some extra red tape and transfer fees.