Sindorim to Gangnam CALT is an extreme backtrack. You'd be wasting an hour each way...and still another hour to get to the airport. Just stick with Line 2 to Hongdae and transfer to AREX. It will take you around an hour from Sindorim to the airport.

There is no business priority security line at ICN. In my opinion, 4 PM airport time is just starting to get busy for evening departures to SE Asia. Shouldn't be too bad. Just stay away from the security near Chinese airline counters. Seriously. They're the largest tourist groups to come here, so if they have a bank of flights leaving, that area will be busy, noisy and a mess.