So today I called my bank in Missouri to let them know I moved, and to give them my new address. I tried to do it when I was still in Springfield, but I never had time.
The bank representative told me that the only way to formally change the address was to fill out and sign a form, which I could do at any of the bank's locations. The problem, I told him, was that I moved out of state and thus no longer had access to any of the regional bank's branches.
In that case, he said, the bank could mail the form to me. All he needed was my new address.
Ah, life. You make a little more sense every day.