I'm afraid I have no specific recommendation. The bank I use is local to central Wisconsin. But I would suggest you have some power here. Think of how ridiculous their position is. It is your money and you are taking the risk. Who are they to tell you how to spend your money. Tell them this is what you want to do and if they can't do it you may need their help in transferring your business to a better bank. In your situation this may not be possible, but if my bank told me that I would give them an ultimatum and be prepared to close out the account as soon as I can set up a new one.
There are many banks and if you are dealing with a licensed exchange then their is no excuse for keeping you from using it except THEY simply want to make choices with YOUR money.  Unacceptable, IMO.