Too complicated. If they're willing, you can once again deposit a small (unique) amount they specify from (the same) address to the address like beforw. I think that's enough to prove the ownership of the $500 you deposited previously.
I'm also willing to do this.
There is no reason to do this and you don't have to send them any proofs, everything they need is already on the blockchain.
All they have to do is to look up the recipient address on any block explorer and they will see that they, indeed, received the ~$500 you sent to them.
It's a shame but it's clear from the response of their customer support agent that they don't even the basics of how cryptocurrencies work: asking for a receipt from an exchange! Don't they know that people can use personal wallets too?
Then saying you could have sent btc to an eth address! Just give me a wallet which can let you do that!