Not sure about Lake Havasu, but when we went down to the Quartzite Rally last year (Jan. 2015), we had reservations made at the Grand Canyon for two nights, but the park wasn't even half full, and we just pulled in to KOA's on the way down there from Colorado and back and was able to get a spot for the night, and none of them were anywhere near half full.
If you get away from the popular spots you probably won't have an issue finding a site.
By the way . . . see you at the Havasu Rally!