Give BaseOps or Universal Aviation a call. They can plan and arrange fuel and handling anywhere as well as diplomatic overfly etc. They will charge, but maybe seek sponsorship from them and explain the cause.
It's probably worth the expense saving the hassle.
Passed thru Cassidy awhile back, don't recall seeing AVGAS there at all. Refueller can be hard to get ahold of at times...
Does a route from Nadi to Funufuti NGFU, Tarawa/Bonriki, Majuro, Honolulu work for you? Fairly sure there will be AVGAS at those places but BaseOps/universal can confirm.