You can get the EG Sim at any GS25 (or at least definitely the one at Incheon - there is a big display of them facing the outside of the store). You do have to get it authorised by submitting a pic of your passport and some other details via a form online (instructions are provided with the SIM). You'll need to use the internet to do this, so use the free wifi at the airport.

They only do the authorisations during business hours, but it's usually pretty quick - definitely not three days. I arrived at ICN after the authorisations ceased (9pm or so), and set it all up, was authorised by the time I woke up the next morning.

Coverage was excellent and had no problems with it at all after the slightly painful setup procedure.