Your thinking has many curious gaps! e.g.,
I fail to see how "shortwave radios" would be particularly useful for the 20 minutes of "nuclear retaliation",
Bitcoin transactions require networked computers which, again, won't be around w/o power/batteries, a working network, etc.
Implementing the Haber-Bosch process requires very sophisticated engineering, machining and careful operation. Lots of trial and error is involved.
simply making "cordite" is only one step in producing an artillery shell. There's the gun, it's transport, the shell casing, the primer, the aiming mechanism, etc. You must train the gunner, etc.
That "organization that defeated Japan" you speak of would most likely not be present (would be destroyed),
No need to kill everyone in China. Just the "A Ship" and they're all in Beijing. Pollution is bad there already and would be even worse after a nuclear war!8-))
One person can "snuff out" a group.
Why do I get the feeling I'm talking to a child who is fairly well-educated but has a patchy understanding of the real world, someone better at history than at science? Maybe someone who games a bit? I think I'll stop this dialogue here.