Unless you wanted to open a United card, spend $2500 on it ASAP (in order to get you to 32,500 miles, which is what you'd need to book a one-way saver award from JFK>ICN), your best bet is prob to transfer your MR points to Aeroplan and book a one-way for 50K miles.

I did a quick search on Aeroplan, and there is availability in August on multiple days. Some options are better than others...for some (that I looked at), there is a 19 hour layover in Toronto, for others the layover is only a few hours.

I would book soon. August award availability to Korea can be difficult (in my experience...although we only really fly KAL to korea, so we don't have quite as much flexibility).

Edit: just FYI, I did search on United and there is a lot of saver award availability in August, if opening a United card is an option for you and you wanted to go that route.