Thanks! I corrected my airport codes but probably as you were replying. And now I have edited the ones I missed.

Fiji Airways is Oneworld and I can get a valid and priced trip with CHC-NAN.

Yes the LAX-GOT offers via LHR.

STO - Stockholm so should be ARN

But my problem is not being allowed to stop in HEL at the end of my trip because the Oneworld tool says I am not allowed more than 2 stopovers of more than 24 hours in my starting continent. My dates only have one stopover of more than 24 hours in Europe (HEL) so I do not understand the problem.

Full list of flights that does NOT work
ARN-DOH
DOH-AKL
CHC-NAN
NAN-LAX
LAX-HEL
HEL-DOH
DOH-ARN

Full list of flights that DOES work
ARN-DOH
DOH-AKL
CHC-NAN
NAN-LAX
LAX-HEL
HEL-ARN