Nope, this is a much different solution.
I quoted the following portion of your post
When you are done parsing the block list, you will have the minimal set of valid and unspent out-points.
That's exactly what a balance sheet is. As long as everyone agrees on this list then transactions work fine. Why store anything else? The block chain is merely a device for ensuring the integrity of this list. Why not just download and store the list, verify its hash in the block chain on startup along with a sufficient history of block chain to be confident it's not falsified?
This provides superior bandwidth, disk space and privacy to your scheme.
The general public doesn't get to see any transactions or balances.
The public has to see the transactions to verify them, the balances can be calculated from them. I'm neglecting your embryonic scheme involving not incompletely broadcasting transactions due to unresolved obvious security problems.
If you want to provide more privacy you could always change transactions so that nobody can tell who the recipient is and how much until the recipient spends the money.
At the moment the beneficiary of a transaction is a certain bitcoin address. If that address has ever received coins before then everyone knows that all the money is in the same place. Alternatively, that address has been publicized as a receiving address so you know exactly where the money is going.
Instead you specify that the recipient of the money is the address that can decrypt a certain message that you have signed. So your transaction would comprise a load of signed TxIns and a signed public key encrypted message saying how much of the BitCoins goes to the person able to decrypt the message. All the network nodes try to decrypt the message with each of their public keys. The one who succeeds knows that they have received the money and updates their displayed balance accordingly. When the recipient decides to spend the money their transaction includes the decrypted message. Only when the other network nodes see this do they know who the recipient was and how much the transaction was worth. Any change is ascribed to the signing key and the decrypted message and original are cited when the change is spent in subsequent transactions.
I wonder why transactions weren't designed like this in BitCoin from the start.