A few comments.
You need to count all flights & distances. Not just the departure & arrival airports you want to visit
Not sure if you have to include "ground segments". That is include things like DRW-ADL if you fly to DRW and from ADL
AUK is in Alaska. AKL in New Zealand (a common error)

BA do not fly MAN to SIN. So needs to MAN-LHR-SIN (as you noted). Or just start in LHR. Starting in INV means no APD

SIN to DPS on MH. Does MH fly that non stop? Or SIN-KUL-DPS.
Wikipedia for DPS does not show SIN-DPS MH non stop.. https://en.wikipedia.org/wiki/Ngurah...tional_Airport
SIN to KUL can be done by rail or bus.Or fly with a range of airlines
Anyway SIN-DPS would be a cheap cash ticket with many LCC airlines.

Map 1 segments
A map from the Great Circle Mapper - Great Circle Mapper

Map 2.
Tokyo to Vancouver on AA will need to be via LAX, ORD what ever.
Be careful with Tokyo airports NRT & HND.
CX also fly into YVR.
https://en.wikipedia.org/wiki/Vancou...tional_Airport

http://www.gcmap.com/mapui?P=c%3Ared...=bm&PW=3&DU=mi

Fares are distance based. So you can fly AU domestic flights provided you keep under the limits (26,000, 29,000, 34,000 or 39,000 miles)
Unlikely you will get under 26,000 miles. So that leaves 34.000 in D class (business)
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