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Christmas Island is West of Australia, so I'm not sure the routing is Hawaii to Christmas Island. The problem is 100LL West of Hawaii...but plenty of H2O.
Personally, the safest way is Alaska, Russia, Japan, Philippines, Indonesia, Australia. But like I said before...you'll need to pay fees unimaginable in the Western world (and bribes too along the way)...and did I mention no 100LL in most of these places past Alaska. Sure there might be 100LL at a very few select places in Japan and the Philippines, but you'll need more than there are stops available.
To answer the question about the N number...the answer is you need an FAA annual to fly that aircraft anywhere in the world, under ICAO. For example, in the UK it is very expensive to own an airplane; so, about half of the general aviation fleet in the UK have N numbers instead of the UK's registration....then FAA registration rules apply, and is cheaper to maintain. I've seen it when I lived in the UK.
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