Skyteam's Korean Air have round trip airfares travelling from Washington DC (IAD) to Singapore (SIN) for $556, making 1 stop in Seoul Korea. The stopover is an overnight, 21 hour layover.
Departs IAD: Sept 11, 12; Nov 13
Returns: Sept 16, 17, 23; Nov 18, 19, 20, 25, 26
Use the above date and book on Expedia [expedia.com]
. Bundling hotel with airfare will save money.
Airline Website [koreanair.com]