I'm using Blockchain.info's api:
I understand that it is impossible for a transaction to know which block it will be included in but maybe one could use the block height to match the tx to the block?
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but maybe one could use the block height to match the tx to the block?
Indeed that would work fine,
block_height is returned by the /rawtx/ call (https://blockchain.info/rawtx/$tx_hash) for transactions that have been included in a block (unconfirmed transactions have no block_height key). Then you can find the block hash and/or information about the block with the /block-height/ call (https://blockchain.info/block-height/$block_height?format=json)