The sleeping medicine is a good idea, and one I haven't thought of yet. Dramamine doesn't normally do it for me. Korea doesn't offer much in terms of pain medicine--a friend had an appendectomy and couldn't get more than Tylenol.
Unfortunately at 23 and in my career of wandering English teacher, a J seat is out of my budget.
I've had mixed results asking at check-in counters and the gate in the past; with a doctors note I was hoping it would be something more solid. Normally I travel with my girlfriend (who's not tall), so hopefully traveling by myself will help.
Thanks for the thoughts.