Quantum Resistant BTC-transactions Without New Cryptography?

Here my proposal/idea: Every BTC transaction is split into two parts: (Before you read further there is an unsolved issue with this approach. See discussion below.)

Step 1: You create a normal Bitcoin transaction without broadcasting it. Then, you take a simple SHA256 hash of this transaction and create a simple "verification transaction" that only contains the SHA256 hash of your real BTC transaction (For creating this "verification transaction", you just use one of your addresses that holds no Bitcoin at all. The nodes and miners will check this verfication transaction" just as a normal BTC transaction today. Writing this verification transaction into a block is necessary to make sure that it can not be modified afterwards.)

Step 2: After the first confirmation of your verfication transaction, you broadcast your real BTC transaction (which looks exactly as a normal BTC transaction today.) The only difference is it that this real BTC-transaction will only be included in a block, if the miners find a matching verification transaction with the correct SHA256 hash for the final BTC transaction in one of the preceding blocks.

For this simple method we don't need a new quantum resistant cryptography. For a quantum attacker it makes no sense to change the verification transaction because he does not know which BTC transaction data refers to the SHA256 hash which was published on the blockchain. And if the quantum attacker tries to change the final BTC transaction than the SHA256 hash of his modified transaction would not match with any verification transactions in the preceding block and will be rejected by the miners.

What do you think? Could this work or did I miss something?