Well, these two are somewhat mutually restricting but how's this for a first approximation:

jfk-nrt-icn-syd//mel-bkk-fra-lhr-fra-jfk

This comes to 27 945 on the GCM. It gives you

JFK-NRT on NH
ICN-SYD on OZ
MEL-BKK on TG
BKK-FRA on LH
FRA-JFK on SQ

or five longhauls on five different *A carriers.

Much tinkering possible, of course; as I said, first glance.

cheers,

Henry