Because of the time until your current permit expires, submit a single renewal form. Don't worry about the change of address. Do this in the county you move to. Do nothing for the previous county.
http://www.vsp.state.va.us/Firearms_ResidentConcealed.shtm#RenewalPersons who previously have held a Virginia resident permit shall be
issued, upon application, a new five-year permit unless there is good
cause shown for refusing to reissue a permit. The same fees and time
constraints apply in the instance of renewal. Persons who previously
have been issued a concealed handgun permit are not required to appear
in person to apply for a new five-year permit; the application for the
new permit may be submitted via the United States mail. The circuit
court that receives the application shall promptly notify the applicant
if the application is incomplete or if the fee submitted is incorrect.
If the new five-year permit is issued while an existing permit
remains valid, the new five-year permit shall become effective upon the
expiration date of the existing permit, provided that the application
is received by the court at least 90 days but no more than 180 days
prior to the expiration of the existing permit.
As far as your NFA stuff goes, you're not required to notify the BATFE of intrastate moves or transportation of registered NFA devices within your home state. You can if you wish, submit form 5320.20 if you so desire, to notify of a permanent address change in state. If you move out of state, the 5320.20 is required.