1) AFAIK, bitcoin has "comments" within transactions. Why not embed the checksum as a comment in a transaction between wallets you control?
2) In the approach described here, no coins are being sent with the transaction (right?). Are blockchain participants really accepting NOP transactions involving 0 BTC transfers. Maybe I missed something.
3) As others pointed out, requiring the whole file to be uploaded is a non-starter for anybody savvy enough to be using this service. Users should be able to directly specify the checksum.