I unscrewed the lockring, and *both* BB cups rotated - what's going on?
This a request for clarification rather than an answer (sorry, I don't have enough rep to comment yet).

First thing to assess is the threading of the right cup.

I assume the BB is English threaded, because it's a CB product; if this is correct then when you unscrew the right threaded left cup, the left threaded right cup would rotate in the same direction, hence would unscrew itself. Can you see a gap developing between the frame and the right cup when you unscrew the left cup?

If my assumption were correct, the fact that they do not rotate more than 20 degrees might indicate that there's some sort of connection (intended or not) between the two. By unscrewing both sides simultaneously you are stretching the connection, hence the block at only 20 degrees.

Finally, sorry if the following comments sound offensive. Depending on your experience in bicycle repairing:


are you sure you are not rotating the whole eccentric when you rotate the cups? I can see you have an eccentric in your pictures.
you might be surprised on how much strength one needs to unscrew old BBs, so when you say "won't easily rotate", what do you mean exactly? Are you applying strength with the arm only or are you using your body weight?


Cheers