Once confirmed, GDAX can't help you.
Kraken can, but they show this:
This is what Kraken answered to someone who sent them 14.2 Bitcoin Cash (currently worth over $40k) in August:
"You are absolutely correct about us possessing the private keys in this circumstance. That being said, it isn't as straight forward as you might think. Kraken is a cryptocurrency exchange and the nature of cryptocurrency exchanges are wholly different from the experience you might have with a personal wallet where you have easy access to the private keys. With things like the theft of Mt Gox, the internal compromise of Shapeshift, the social engineering of BitPay, and others, we must put security as the paramount concern. As such, our exchange is setup in such a way that nobody within Kraken can unilaterally move funds. We believe that this is a very important protection that makes it extremely difficult for client funds to be stolen by external or internal parties.
Only a very small group of people at Kraken (devs) have the ability to access your funds given an auditable thorough process of checks and balances. This makes the process extremely resource (time) intensive for the devs that have very full plates and very little time to dedicate to any specific task. They must prioritize all of our tasks internally and the requests of clients as best they can. We think that the prioritization of improving our UI/UX as to avoid these type of mistakes will show the greatest dividends for our clients."
I understand their reasoning, but the amount of money lost keeps increasing. In the future, with enough public pressure, maybe it becomes possible for exchanges to recover cross-chain-deposits once a year. On a specific day, they outphase all deposit addresses, start using new ones, and after some time to overlap, the old private keys can be sold to the account owners if they want to recover anything from other chains.
In theory, your coins are sitting on the BTC blockchain in the same address you sent the BCH to. So who owns the private keys of these? if im not mistaken, nobody does.
Kraken owns the private keys, both chains can use the same address, and they come from the same private key.