Not sure about the county as a whole, but I'd guess Mongomery County will sign (SW VA, contains Blacksburg and Christiansburg). Specifically, Cheif Brown of Blacksburg will sign. Make an appointment, show up, sit down, he signs them, shakes your hand, you leave. Apparently you can leave them there, but he prefers a face to face for at least the first one. From what I know, he likes to sign them, but he keeps a Xerox of at least one F4 so he knows who in the area has something. Its a big folder I'd guess and I don't think it goes anywhere except into a drawer. I don't know the legality of that (without the tax stamp, it was just a form with a signature at that point), but I wasn't going to look a gift horse in the mouth when he was willing to sign. Besides, I changed addresses later...
I had both F4s for my silencers signed in less than 10 minutes and that included a short chat about how/why the Blacksburg Police converted to GLOCK .40s.
From what I understand from a guy at the Roanoke RPC USPSA matches, the Roanoke CLEO will not sign an F4, but you can take it up the line to a prosecutor (Comonwealth's Attorney?) who will sign (it took him only a couple weeks to go from non-signing CLEO to signed F4 for his NFA toy).
--Jeff Chock