Hey look at that! Conflict-resolution! 
Yes, Discworld would be a good comparison for the silliness, and it has a benevolent dictator
I'll just lean into the sinister aspects of matriarchy. I remember an interview where Chuck Palahnuik said that his writing-students always try to solve the problems in their stories, and he has to tell them, "No, don't solve it, make it worse!" Resolving tension leaves you in a serene greyness – you should be trying to intensify it. And I already risk making the queendom a utopia, the more tensions I have in there the better.
The guard's name origin is from the Queen (UmbraVivi's first thought). She builds public libraries in pink and issues coins like the Gold Daisy and Silver Star; everything official to the state should be girly to the point of annoying. Like imagine Princess Peach is in charge.
Now the reveal: literally the only reason I started this thread was to see if anyone had heard of Benjamin Disraeli's Primrose League, or if that was obscure enough to be ignored. Fifty comments later I have my answer.
The south of the Polynesian triangle u mentioned gets into the Roaring Forties (eastward wind).
You can ride that all the way to America: "Hacia 1837, un grupo de ingleses, sin conocimientos de navegación, escaparon en una pequeña goleta del asentamiento penal de Sarah Island, en Tasmania. La corriente y los vientos los llevaron hasta Chiloé, y luego subieron hasta Valdivia." – Chiloé and Valdivia are south of the Inca Empire, in Mapuche territory.
I think it's defensible to say: "Chinese treasure junks + Polynesian knowledge of sailing near NZ = riding the Roaring Forties to America"
The Mapuche and the Inca were just prior to fighting a war at that time, so Chinese contact would doubtless affect that somehow.
PS: Once they hit that, it's a handy ride to the Inca Empire: https://en.wikipedia.org/wiki/Humboldt_Current