It may take as much as 6 months to a year to get the plates. At least it was like that to get my caps plates
From what I've read about the process, I believe the way it works in Virginia is that the 450 applications are a prerequisite and then a bill allowing the plates has to pass the General Assembly. If you look at the online bill tracking system you can usually find a few dozen bills every year relating to special license plates. They're invariably consolidated into a single bill covering all of them; it then passes and the Governor signs it. (They almost never reject a plate design in part because they're concerned that the ridiculous number of special plate designs may have given rise to a First Amendment right to have most plate designs allowed. Consider that other states' attempts to reject plate designs, such as the Sons of Confederate Veterans in Maryland, have been overturned in court.)
So passing the General Assembly is routine, but it does take time because for obvious reasons the license plates are, and quite rightly should be, a fairly low priority. Then there's some issue about the time it takes for the DMV to have the blank plates manufactured and then to have the actual numbered plates issued.
The whole process of having your law set up so that the General Assembly must authorize each special plate design is a bit absurd, IMO, but that's Virginia law for you.
I believe I saw something on the Nationals' Twitter feed a few weeks back saying they passed the 450 applications a while ago.