This is a bad idea. Not only are you misusing the 5320, you are misusing NFA Branch resources.
The 5320 is not a change of address form, it's an application for interstate travel. [cans & AOW's are excluded] ...
.... Submitting a 5320 application mistakenly identifies your request as a higher priority action when such requests would more properly come in the form of correspondence.
If you feel you have to tell them that you moved down the street, then send a letter stating that. Don't present it as something else.
We're all waiting [strike]5 months[/strike]
9 months now for approvals. Wasting their time is wasting our time...