I haven't traveled that route in years, so don't have any current advice, but I'd like to point out that reservations don't have to be made weeks in advance and limit your flexibility. Even busy campgrounds usually have a couple sites available for whatever reason, but they get snapped up quickly by early drive-ins. With cell phones, laptops, and navigation systems, it's easy to project where you will likely be the next day and to identify campgrounds in that area. Call ahead the night before and make a rez for the next nights stop. That greatly improves your odds of finding a place that suits your needs.
Another factor for no-reservations gamble is the time of day you expect to stop. If you generally stop by mid afternoon, your chances of getting a spot are much higher than at 6 pm or later. If you expect to be driving until later, reservations are strongly recommended in a bust corridor like the 101.