To prove your pdf existed, I would go a similar route as you took: I would hash the doc, convert the private key to an address and verify that the address has received money in the past. If it has, either the document must have existed or the extremely unlikely event that someone chose the hash of the document as a private key by accident must have happened. Since we can rule out the latter with high probability, the documents existence at the time of the transaction is proven.
Please note: you should move the money from that address. Anyone with the document can access it.
Excellent! Thanks.
you should not move all money from that address as the bitcoin paper describes pruning of transactions from blockchain for empty addresses. if you need your proof to be preserved longterm this is a risk to be aware of
This is a valid concern and I've thought about that: I think it's save to remove the money. There will most likely always be a complete transaction history available and it's good practice to keep the unspent transaction output set as clean (small) as possible because it has to be accessed quickly by servers/wallets.
Also: you'll have to keep the document itself anyways. So why not keep the block with the relevant tx in it along with it?
EDIT: another minor point: If you're concerned of losing the ability to prove existence due to the money being removed from the address, you would also have to keep your document secret to avoid someone else removing the money.
EDIT2: sorry for all the offtopic babble.