How does it look? Pretty hopeless I'm sorry to say

Your issue is that no Oneworld airlines fly between a number of your ports, namely:
ANC-LAX and LAX-ANC (AA does not fly this route - it codeshares on AS and in general codeshares on non-OW airlines are not allowed)
LAX-PPT
PPT-AKL (QF codeshare on TN not allowed)
AKL-NAN
NAN-SYD

The rest of the itinerary is OK (SYD-MNL-HKG-DPS-HKG-SIN-CMB-AMM/NBO-LHR-LAX)
and BTW RJ flies between AMM and NBO

The rules of the ticket are here

There is another RTW ticket called the Global Explorer; its rules are here. It would allow all the flights on your itinerary, BUT it is a mileage-based ticket and your itinerary well exceeds the maximum miles allowed.

ps Welcome to FT