At this point, it's interesting to speculate on what comes next.
Obviously, the best thing to do in a hostage situation is to stage a successful rescue mission. That, though, would mean that this story line would function only as entertainment, and not make a point about how AnCap works. So I'm assuming that this won't be possible.
Still, they are going to avoid the alternative of sacrificing one individual versus surrendering their whole society to slavery. They must do that, and yet they need to do it in a way that doesn't seem like a cheat to the reader.
Embedding a hidden message in the provocation somehow that negates it at a later time is one clever possibility.
Another is to give them their provocation - and then defeat the subsequent full-scale military assault on the Belt. But if they can do that, the main source of suspense in the story all along was pointless.
And the thing about kidnappers, too, is that you can't really trust them to release their hostages unharmed.
Now, if the Black Mamba were really a worthy adversary...
she would have lied about where Kate is being held, and the staged provocation would be misdirection, just to torture as well as distract Ed and the other Belters. The real provocation that's going to be televised on Earth is the attempted rescue mission against the runabout!
But I think the Belters are smart enough to consider possibilities like that in their plans.