Yes, Kamakura is probably the best time within the SCA's timeframe for doing any kind of plausible strong female persona - I have an article about women in the Kamakura that I'll email you.
The SCA requirement for Asian personae to be visiting European holdings is kind of a pain in the ass, especially before the Portugese showed up, but wandering off through Mongol territory from Hakata is as likely a way to get there as any, I'd say. It really was a quite well-connected trade port as far as ties to the rest of Asia go, and so you can always have intended to take a look at somewhere in China, Korea, or Mongol territory and then just kept going until you reached Europe. Travel Hint - "Mongol age" section of this article on the silk road.
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The SCA requirement for Asian personae to be visiting European holdings is kind of a pain in the ass, especially before the Portugese showed up, but wandering off through Mongol territory from Hakata is as likely a way to get there as any, I'd say. It really was a quite well-connected trade port as far as ties to the rest of Asia go, and so you can always have intended to take a look at somewhere in China, Korea, or Mongol territory and then just kept going until you reached Europe. Travel Hint - "Mongol age" section of this article on the silk road.