4:20 should be plenty of time for your connection. You'll have to clear immigration and customs at ICN, but it's usually very efficient. As a USA citizen you are permitted to enter for, I think, 30 days without a visa.

I agree with planemechanic's suggestion to use the bus. It is inexpensive, runs frequently, and takes about 30 minutes between GMP and ICN. There are actually many bus lines that connect the two airports. Take a look at http://www.airport.kr/airport/traffi...ist.iia?flag=E to see. Buses depart from just outside the arrivals hall.

The train seems like a decent alternative. I haven't used it yet since the train links were only completed recently. I've taken the bus many times.