[brazzy]

Did they have someone in the camp with basic knowledge of Chinese orthography?

This is definitely a possibility, but even then...

> Did someone know enough to note carefully the way in which the characters were written? Did they keep the paper with the characters on it, and then hand-reproduce the precise structure?

This would be unlikely to work, because the characters would be written on paper using a pen or pencil, which produces quite different strokes that a brush, which is what you would have to use for a sign. Even if you know how brush strokes should look like, I can't really say how difficult it would be to produce brushwork that credibly looks like what someone would produce who has been doing it all their adult life, if you lack the experience.