Can anyone explain why the signing order is important? i.e. Why can the nodes not just sign to release in any order?
To keep the code that checks the signatures simple and fast (remember that it must be checked by every full node in the bitcoin network). Suppose you have a 14 of 15 signature. If these were not ordered you have to check every signature with every key, in the worst case more than 100 checks. Since the protocol requires that the signatures are in the right order, you only have to check each key once. If it doesn't match the signature at the expected position you immediately know that the signature for that key is not present.
Also, its easy for a signer to put his signature at the right place, so you don't have to really sign the transaction in the right order, you just have to order the signatures right.