The new transaction will have to change, because as said, it will be rejected. You can slightly change the locktime value to one lower, and it will produce an entirely different hash. If you don't want that, you can pay 0 coins to OP_RETURN; that will also work, but it'll cost more.

This is not OP's concern. His concern is: what happens if you have two transactions which have absolutely no connection but produce the same TXID? And the answer is that the second will be rejected, because of the BIP 30 soft fork.