Assuming you have the xprvkey for M of your N keys, then you just need to find the UTXO for your funds and publish a transaction that moves that to another key.

We list all UTXO for your account (with all the transaction hashes needed) in what we call the "audit report" and that includes multisig accounts now too. The subkey needed (M/x) is indicated in that report as well. Armed with that information, a site like ms-brainwallet can produce and send the transaction you need.

Also for you doomsday planning: we email a copy of the HSM private keys associated with your multisig account, encrypted with Coinkite master key that would be published after we shutdown. (Very similar to what we've always done with regular accounts).