I've attempted to challenge a few nations to danmaku duels but always have to back down because it turns out they're way stronger than me. I have a diplomatic skill of 6, near 100 prestige, one subject, and 7 diplomatic reputation. I'm guessing the problem is my danmaku power and/or danmaku power modifier, which I have no idea how to check or even improve.

I have no problem with the normal incident duels, though. It's just in the diplomatic ones that I'm outmatched, even against "weak" opponents.