Perseverance, I haven't actually camped there, but have also been looking at google maps for free places near Parker. Last winter, someone told me about the Parker Strip on the "California" side. There appear to be some spots right along the river on the CA side, a mile or 2 north (Parker Dam Road) and south (Rio Vista Drive) of the bridge.
On the AZ Side near Parker, it appears to be mainly private property and Indian reservation. There is a lot of space around the Blue Water Casino, but it may all be indian property. A little ways north is La Paz County Park, which is pay, but where van people go for showers.
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http://www.lapazcountyparks.com/
Maybe you could check them out, and report back.