cheapest time to fly

Cheap fares would depend totally on the airline and can often be hard to predict. Usually the further out the cheaper.

Your low season estimate is probably about right, but as for the cheapest time to buy, as per westwoods comment - no hard and fast rules and if fuel prices pick up over the coming months so will seat prices. I'd pick out the airlines you'd be considering and check them out over the next couple of months and see if there's any trend. Typically I'd buy a couple of months ahead but on the low end of the market there's probably not much in it and you'll find more variation between day and night flights. Rarely is last minute the cheapest option, but you might get lucky - and then again you might not.

Beware of Chinese new year and Cambodian new year when prices up and need to book

do some searches for fares on different dates and note that apart from the above different airlines have slightly different dates for off -peak

Sometimes there will be offers but usually best to buy early

The prices start going up 1-2 month in advance, so if you purchase at least a month ahead, you should be able to get a good price. Otherwise avoid Christmas and New Years, Easter and Chinese New Year as well as any major Korean holiday and you should be able to get a good price.