There might be a provable way to destroy their CNP deposits too, but I have to think on it.
I think there is. Evil CNPs won't fall for it, but it is a huge indication that they are evil, and this still works.
CNPs don't need to sign all communications with all peers--such as regular tx activity, but it will sign the hash of each TB it receives with a timestamp and some indicator of whether or not it believes it has been received in time and whether or not it agrees with that TB's state of the network. This is some algorithm that can be rooted in the 10 TB window or whatever, I don't have the exact mechanism yet.
If a CNP refuses to sign a TB that a client has seen from another CNP or from the shadow peers, the client can essentially immediately ban that CNP.
Hilariously enough, because the honest CNPs will do this, the dishonest network could destroy their deposits in a dishonest half of the network--but this would be a huge indication that the
those CNPs are honest. For evilcorp to perform the reverse attack, the attack
must be done in secret. On one side, all people watching know, on the other, no one watching knows. There must be a fully connected alternate network operating in secret. If it is a legitimate network split, things are hazier, but not unfixable. Unfortunately it may have to boil down to some kind of voting protocol to accept the network splits back in without penalty. Presuming it was an honest split, which should be so incredibly rare anyway, but the reasoning should be world news, the networks have every incentive to get back together peacefully and without penalty if there is a legitimate reason for the split. The money supply will be doubled if they don't. This applies to SHs too.
It gets back to whether or not EvilCorp can continue to fool everyone over an extended period of time. If someone receiving a tx that is intended to be double-spent, and it has confirmations from CNPs who acknowledge and accept the block the tx is in as the state of the network, the person who is potentially being defrauded has evidence that he is on an honest network. Even if those CNPs are evil and plan to reneg, if they accept some forked chain at a later time and ignore those signatures, their CNP deposits can be destroyed on an honest network.
This makes the CNP portion of the network much more powerful and reliable. I think this can work really well.