From Incheon to Gimpo - No hassle.
From Gimpo to Conrad station (on metro line 5) - it got a bit stretched on the last 6-7 stops, as it was packed with people going to job. Had no issue to get off though with 1 large suitcase, one backpack and one small suitcase.

I would try the alternative, which is to take the train all the way to the end, and then use the subway only for 3-4 stops.