Semantically that is problematic. You don't know who the person who successfully mines the transaction is going to be so there is technical no "output" to give

Semantically that is problematic. You don't know who the person who successfully mines the transaction is going to be so there is technical no "output" to give it to until the block is mined. Perhaps an extra header field with the fee amount that needs to match the unspent inputs would work. Edit: and as another commenter pointed out, if you set the output to someone other than the miner you are doing a 0 fee transaction which is discouraged and in bitcoin, highly unlikely to end up in a block.