If you travel a lot back to the States, plus a lot to South East Asia, you can save considerably on your airfare if you can plan in advance and book tickets that include the USA and South East Asia, with Korea just being a long stopover. I do this all the time, and often pay about the same or less for the whole ticket than I would for just the Korea-USA portion. Of course if you're working for a hagwon, you might not be able to plan your schedule that much in advance, or be guaranteed you'll even be working there in the future after your contract expires.

I fly OZ but imagine it's probably similar if you were flying with KE. In the past I'd book the cheapest full-mileage earning class ex-USA, with a month-long or so stopover in Seoul, then continuing on to wherever it was I wanted to go in South East Asia for my vacation, followed by another long stopover in Seoul on the way back. Then do it all over again. These days I'm traveling to Thailand about every month or so, and ended up switching to buy my tickets ex-Thailand, with the stopovers in Korea, then to USA. It works out a bit cheaper that way, though not a whole lot. When I want to visit some other place though, I end up buying a separate ticket ex-Korea, which probably overall increases the total cost, compared to if I continued to buy the tickets ex-USA. Anyways, fares ex-Korea on KE or OZ are quite high, whereas fares ex-USA or ex-South East Asia are pretty cheap. For instance, you mentioned 800,000 KRW to SIN/KUL. I often pay roughly 1,300,000 KRW equivalent for R/T tickets BKK(or HKT)-ICN-LAX, meaning the transpac portion only ends up costing me something like 500,000 KRW when compared to if I'd purchased it separately and paid 800,000 KRW for the South East Asia portion only. It works out well for me, but requires a lot of advance planning that's not always easy to do.

Sometimes I don't even need to be traveling on one portion of the ticket (either the transpac or the South East Asia), but I love flying and love racking up the miles, so don't mind doing a trip with an immediate turnaround or only staying a single day before returning. That was a bit of a problem though when purchasing tickets ex-USA being the cheapo fares sometimes had a minimum stay at the outmost point, and I wouldn't be able to stay that long being often it was just for a day or weekend. But buying my tickets in Thailand solves that problem being they don't have that restriction, nor do they even have any fares that aren't full mileage earning. I don't know though if KE is the same or not.