Support for verifying Korean summoner accounts was removed by Riot, and their current policy specifically prevents any attempts to otherwise verify or circumvent this limitation. This change is beyond even Riot games, and more details can be found on this post in the developer discussion board:
We're sorry for any inconvenience caused. Remember though that you can still view your summoner on our site. You just can't verify it. Should you have any further questions or concerns please open a support ticket above.