1. Look at possibility of codeshare flight. If you can change your flight to QR codeshare, then you should credit to AA.
2. If most flight you can change to AA/BA/IB market flights, then credit to Finn air.
3. If most flights you can change to JL marketed flights, then credit to AS.

Note: Change to codeshare flight is free if you booked from AA RTW.

Just search around what codeshares are available for all your current flights.

AA points worth a lot more but harder to get OWE. Avois does not worth a lot, and possible to get OWE for one RTW