Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
Here's what I would do:
1. Get some BA Avios.
2. Fly OMA-Europe on an AA award.
3. Fly Europe-ORD (stop) - Hawaii on an AA award.
4. Fly Hawaii-OMA on an AA award.
5. Use BA Avios for the ORD-OMA-ORD segments: only 9,000 Avios needed for the roundtrip. (As an alternative, you could fly Southwest MDW-OMA-MDW, but I think that the change of airports in Chicago is a hassle best avoided.)