Technically you don't need one. You're traveling from one legal place to another. However, September is plenty of time to get a 5320.20 approved. And you never know, you might want to go to a shoot in VA some time in the next year.

So pick a range in VA and file a form using that address, and do it for a 1-year period. It doesn't cost you anything, and you have it if you need it. And then you know you're covered while passing through.

I routinely file for every legal state near me, plus any other state I think I may want to visit in the coming year. Just in case.

5320.20 is never a bad idea, if only to placate some Barney F.  
The extreme lack of NFA knowledge throughout much law enforcement is seldom advanced with undocumented verbal debate on the roadside.

An alternate solution often mentioned, if the platforms allow, is to put a 16" upper on the SBR lower, and move the short upper to a pistol lower during transport.

I would do it anyways.