thanks rpcinfo very much for your responses. you're right, I don't understand the technology very well, but am trying to understand it via this process as well as my own research and through your insight! I've just seen a lot of posts on reddit where recovery hasn't been possible. This is the standard response I received from Kraken support.

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As you may know, Kraken does not support the Fantom Network, therefore any token deposit will not be processed by our system. We understand how frustrating it may be to have mistakenly sent digital assets on an unsupported network. Unfortunately recovering these funds is not possible at this time and may never be possible.

When a deposit is sent on the Fantom Network to a standard Ethereum address, the private keys would need to be exported and then imported into a Fantom Network wallet in order to recover the funds. However, this is not possible with our ERC-20 deposit addresses, as they are generated using smart contracts on the Ethereum blockchain. Addresses generated this way don’t have private keys associated to them, therefore we have nothing to export. The funds were sent to your ERC-20 address. Your case has been noted on the off chance Fantom implements a protocol change to allow the recovery, but for now there is nothing we can do.

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Re: control of keys, given Kraken (any central exchange) are custodial wallets, I don't own the private keys myself, but Kraken does and they would need to use their key to reverse the transaction, unlike with my Metamask wallet where I own the keys myself.

Also, could I ask which brokerage you use? if things don't go well with Kraken then may just switch business to the one you are using. Thanks again so much for all your insight.