The safest way would be doing 1 itn. Since you will have the most protection there. Have you look at JFK-ICN with a "stopover" in SFO? If you stop in SFO on the return, you could "miss" the connection back to JFK. Just make sure that you dont put your bags back on the belt after customs.

4 hrs layover is plenty of time especially a morning flight like this (JFK-SFO). I think you will be fine. If you are not sure, you can fly the night before like you said. You could also rough it in a hotel for less than $100/night as well (doubletree is about $90++ and about 2 miles from SFO - cheaper hotels available).

I am not sure about AMEX. I'm sure someone will weigh in.

drew