If the KE flights are available at low, they can be booked with AS or DL miles, plus other SkyTeam partners such as AF/KLM. However, KE has extensive blackout dates for award travel.

Why do you insist on nonstop? There should be a lot of AA flights (through MIA, for example, but perhaps NYC too). There's a DL routing through ATL. UA probably has service through IAH and perhaps other hubs.