It seems almost certainly impossible (surely not all these routes exist, even if they once did), but you can definitely reduce backtracking with careful research.
POM and NAN are useful hubs. GUM, HNL or even PPG can also be handy options, if you didn't want to avoid the USA.
One gem I found (that you seem to miss in your route!) was Talofa Airways, they fly FGI-TBU (That is Apia CITY airport to Tonga). Of course, you won't find anything searching APW-TBU, even though APW would appear to be the obvious choice for an international itinerary.
The South Pacific is like that, schedules and routes can be hard to research, with sporadic schedules, and can cease without warning. And some islands will pretty much only ever have one flight servicing them. Backtracking for those islands is of course the only choice (unless you charter or go by boat).
Please let us know in this thread if you find any interesting obscure routes.
Last edited by CPMaverick; Apr 29, 2018 at 6:54 am