If you really want to go during a booked-up time, you can stalk the reservation site every day and snag what you can then stitch it together. That's how I did Christmas last year. I think we ultimately ended up with three reservations to cover a week. As long as you are booked for the same level of site (P-Up/tent, Full HU, Preferred, Premium) for all of your reservations, it is very likely that you won't have to move sites.
I just watched and snagged what I could when it came up, sometimes with a patchwork of site levels, but ultimately I was able to get them all as premium. Kind of a pain, and takes some diligence, but it can be done!