I've only had to do this a couple times at full campgrounds, but almost any nice couple in an RV will share their site with you. I offered to split the campsite fee, but they wouldn't hear of it. I'm not very scary-looking, though.
There's no hiker-biker site programs in your area, I guess. It's really nice to have it available here in SoCal. This past Memorial Day weekend, climbed 4000 feet up into the Cuyamaca range east of San Diego and spent one night at Green Valley Falls (4000', 25 F low!!!!), then north 16 miles to Julian for the day, and back S 11 mi to Paso Picacho (5000', windy, 50 F low) The car campsites are reserved many months in advance, but hiker-bikers can stay overnight in the picnic area for $5 at both campgrounds. There's room for a hundred tents, but the ranger said she thinks I'm the only cyclist that ever takes advantage of the deal.
Maybe your local cycling organizations should agitate for the same type of program in state parks; it's great not to worry about a campsite, just about getting up those dang hills.