I found the paper "On the State Minimization of Nondeterministic Finite Automata" which, I assume, contains the Kameda-Weiner algorithm that I've been searching for. It's behind a paywall though. I'm just a hobbyist. Can someone explain it, or point me to another source?
I've never gotten around to describing it, but to be brief, it's very involved. The only way to gain a useful understanding of the algorithm is to read the paper start to finish.