Another possibility is on JL through Tokyo. You can get AA miles if they codeshare on the JFK-NRT nonstop; they do on the ORD-NRT flights. The wife and I did it this summer. From Chicago, the routing required the JL non-stop to Tokyo, overnight at NRT and fly the next morning to DPS with a brief stop in CGK. You can make it back without a hotel stay on the same routing.

Best of luck.