DownTheAvenue said what I would say, don't miss it no matter what time of year.
We have also done Front Royal to Cherokee only once in a truck camper that was 12'2",
once in a 28ft class C, we just hugged the center line and all was fine.
double check to make sure the CG is open you want to stay in, we were there before the GOV cut back and all the CG's were open, we stayed in every single one of them, some would be very tight for a longer TT.
If you go be sure to check out all the cool things to see right on the parkway.