I'd like to explain bitcoin transaction signing in more detail.

1. Bitcoin balance will be secured by bitcoin multisig. 4 of 6 or something close to that.  We will post a detailed security model with risk analysis once we get to implementation. Here is an example of similar work of ours:
https://ambisafe.atlassian.net/wiki/display/AS/Wallet4

2. Ethereum contract will be aware of Bitcoin wallet balance.
3. Once event occurs that should trigger BTC transaction, Ethereum wallet will create transaction as an event, with the BTC address as one of the ethereum event parameters. In this way we are creating a "master record" of what should actually happen.

4. Our multisig wallet server software will be listening to the Ethereum contract events. Once Bitcoin-related event occurs, unsigned bitcoin transaction will be created. All signatories will get an email notification that something is waiting for their signature.

5. Every insurance committee member will sign in and sign transaction sequentially.

6. Once transaction has been posted to Bitcoin network, we can provide a cryptographic proof to Ethereum smart contract that transaction has been executed. Similar thing is already implemented in BTCRelay (https://github.com/ethereum/btcrelay)

We can semi-automate this schema by involving several bitcoin security companies. I'll explain other options in more detail tomorrow.