Although I haven't tried it myself, many forum posters in the past have recommended just riding into a full campground and asking other campers to share a space. Of course you should also offer to split that high nightly fee. This works best in non-commercial campgrounds where the sites are more disbursed and larger. It has worked quite well for many bike tourers. In the campgrounds where we have stopped on tour (New England, Quebec, Atlantic Provinces) there are usually other bike tourers already in sites. I would never hesitate asking to split a site (and cost) with another tourer when the campground is full.
Even at a full state park campground, the ranger may well find a grassy spot for you if you show up late in the day after a 50-60 mile ride. Our camping style has very low environmental impact. Of course, If you ask and the answer is no then it's harder to then ride into the campground and apply the approach in the paragraph above.
Sounds like a fun trip.
Jim