I've got my note's public address, the Letter of Guarantee, the TXID for my deposit, and I can even sign the address I used to deposit if they want. Of course, I don't know how to prove that I didn't get anything back since they haven't made any transaction from their end.
Hopefully you don’t have to do that, but it’s quite trivial. You said have a signed LoG saying you withdrew X BTC to the address Y, all you have to do is post the note and everyone can see through a block explorer that your address hasn’t received the coins.