The row across stream and then back is a no-go. The camps are assigned and across from the put-in isn't on the list.
I would 2nd the Harding Hole hike-in if you're camped there, if you're sure footed it's a lot less than a 45 min down hike. That road is the Yampa Bench Road. It's one of those 4WD roads that a gung-ho driver in a Civic can do. She could probably just park a car, meet you, and you guys could get the car on your way home. Lots of extra driving, but cool views from the bench... I don't know of anyone who could do a drop-off, although Wilkins bus lines might. River Runners Transport only moves cars, not people. Definately clear your plan with the NPS first though. If their head count at the take out doesn't match the put in you'll likely get banned for a few years in addition to paying a fine.