In any case, I feel lucky that I got my money out and will stick to wire transfers for now while I wait for banking institutions to adapt to new tech.
For future reference, the way around this is to insert your own wallet in between the bitcoin exchange (Shakepay in this case) and your Forex broker.
If you set up your own wallet in which you own the private keys, such as by using a piece of software like Bitcoin Core or Electrum, or by buying a hardware wallet such as a Trezor or Ledger for added security, then you can guarantee that you will always have access to the same addresses and they will never expire or be unlinked from your account or anything else that an exchange might do. You can withdraw from the exchange to your own wallet, and then from your own wallet deposit to the Forex broker (or whoever else you are sending bitcoin to). If they insist on only sending bitcoin back to the same address it came from, then that does not pose any issue at all, since you are the sole owner of that address and you can use it as many times as you like (although reusing the same address endlessly is bad for your privacy).