Instead of having one secret i.e. a private key to your address
You now have secret 1 and secret 2
secret 1 is the encoded transaction with private key discarded
You would have to keep it secret as otherwise anyone could just initiate the transaction and we would be back to square one
Secret 2 is your private key to your address
If only secret 1 is completely stolen your coins are lost (unless thief is good enough to process transaction)
If only secret 1 is stolen but you have a copy your coins are still safe but we are back to square one.
If only secret 2 is completely stolen your coins are lost.
If only secret 2 is stolen but you have a copy then it is a race to perform a transaction
If both secret 1 and secret 2 are stolen but you have a copy of both then it is a race to perform a transaction
If both secret 1 and secret 2 are stolen and you have no copy of either then your coins are stolen.
If both secret 1 and secret 2 are stolen but you have a copy of secret 1 but not a copy of secret 2 then the coins are stolen
If both secret 1 and secret 2 are stolen but you have a copy of secret 2 but not a copy of secret 1 then it is a race to perform a transaction
Now we need to to assess the probability of a breach of bank security or super-spy-government-satellite attack or other such attack on each of the above scenarios in relation to the increased probability of key loss.
If we calculate the relative probabilities for each scenario and use this to calculate an overall weighted probability that should give us some idea of whether we would be better off using this system or not.
