I believe that American also flies directly into LIH. I do know that UA flies direct from LAX, SFO & DEN. Too bad they don't from ORD!
I didn't realize that there was an Embassy Suites in Poipu! We had asked if Hilton had anything last fall when we were at HHV and they said no properties on Kauai.
RE *wood points, did you look at the Sheraton Poipu? It seems like most people only look at the Princeville (JMO based on posts in the spg forum). I've stayed there twice and enjoyed it, although not as much as the Marriott Lihue. Not quite as flexible as if you have a condo, but it's a thought...