In the simplicity of Title 12 USC §411 there is nothing said against any state bank redeeming lawful money. In the process and agreements of becoming a corporation though, I would not be surprised if there is verbiage restricting your ability to non-endorse.
The upside is that if you non-endorse your signature card while setting up the corporate account then you get that on the record - your Demand. Even if the bank attorneys tell you to remove it, you have the record if you are careful to get copies as you attempt to implement your demand. Therefore the bank is restricting your (the corporations) rights. However, on the other hand the new corporation is applying for state-doled rights to begin with in return for limited liability. So around and around we go...
As I teach I learn. As I learn I teach.
I come to the conclusion that you are free to make your demand but in context of applying to the secretary of state for your corporation status you may find the options of exercising the demand for the typical expected benefits - full refunds of withholdings - may produce limited results. You are asking to replace the sole proprietor responsibilities with limited liability from the state. I do not see anything preventing you getting your demand for lawful money into the record.
Regards,
David Merrill.