I've lived and sailed in the Okinawan chain for 16 years. The generic information you read isn't specific enough, and it depends on your route. I wrote that July-Sept. is considered typhoon season. October typhoons are infrequent. If you are passage making by island hopping through the Okinawan chain from Taiwan, it's a different story than a non-stop bluewater passage, you are not offshore for weeks at a time, and can linger as needed at an island port (fees are quite reasonable). I speak the language and the fishing-boat ports are protected. October seems possible, depending on use of all the available weather technology. May is not typhoon season, we frequently sail in May. June is the monsoon, and not a time for bluewater passage (not considered a typhoon month, here). the caveat is that in a given year, the monsoon can arrive earlier, later, or almost not at all.
My thought was to find safe moorage in the south by sometime in June, then continue from October or later. We sail in the winter, Jan/Feb., not fun but nothing like a New England winter, where I'm originally from. Water's warm, breeze is often fresh.
Part of my plan involves upwind passage making, so performance in this regard is a real consideration. A decent sea berth, no flat bilges I haven't gotten to mapping precise waypoints and timings, I am three years out. I don't own the Cornell book yet, it's on my list. thanks for mentioning it and Panama. (I'd prefer shorthanded to solo.) There are some wonderful hot springs where I live, and the shochu and nihonshu are divine, not to mention the tofu. About last north in the Okinawan chain is Yakushima, it's a world heritage site -- the entire island. Worth a visit! Cheers.
Ok I agree Mexico may offer some boats though fewer numbers. Likewise Panama for those who toss it in. Try this one Mazatlan Marine Center SA De CV (Mazatlan, Sinaloa, Mexico)
The Baba 30 seems a good boat with the cutaway keel although not quite what you are looking for. It might be a bit slower but not as squirrelly downwind as more modern designs which suits long downwind singlehanded passages.
I don't understand your route if Hawaii is Hi.
The Northern hurricane season is May - October with September the worst.
If you leave in May that would be very late. You also have headwinds after the equator heading to Oceania and need to reach Australia or NZ by November.
Normally you would pick one hemisphere or another and run through the South Pacific then up to Japan by June That would be 12 months. My point is if you do Australia NZ and the islands you then sit out up to ten months broadly, to cross back into the NH by Nov/December. A NZ summer is not bad but it depends if you want to spend 22 months or so on the trip.
There are variations but you might want to look at World Cruising Routes by Cornell for detail.