I am an archaeologist, and am a leader on a natural history float down Deso-Gray this summer. I haven't been on this stretch before, but am doing some research in advance. There is a book, Petroglyphs and Pictographs of Utah: V. 1 (K. Castleton, 1984), that describes some of the Range Creek rock art. Apparently there are also a number of very high cliff granaries. How close they are to the Green is unclear.
Range Creek was part of a high-profile exchange of ownership from private to the State of Utah. It is a unique place due to its high degree of protection by the landowners when much of Utah was being plundered by artifact hunters. They are now apparently allowing some visitation. It would probably be useful to contact the State of Utah (I think Div of Wildlife) for their input. It appears that their ownership does not extend to the Green River, but they could probably shed some light on it. The lower stretch of Range Creek could still be in private hands.
Hopefully you can appreciate the fragility of these antiquities anywhere along Deso-Gray and will only observe them. As the old saying goes, "Take only photographs, leave only footprints."
I have been in the archeology site in Range Creek before on a guided tour and here's what I know. I believe you need day permits as mentioned, but you can only go in on foot (unless you go with a permitted tour company, only they can take vehicles/horses/bicycles in), and the only areas I know of for camping near there are on the opposite side of the archaeology area away from the river (more near the Tavaputs Ranch, who also happens to offer tours of the area). Also, many of the archeology sites there are super subtle, difficult to find and spot (many of the granaries require a spotting scope or binoculars to actually see, they are so high up the cliff walls and blend in so well).
So with that being said, I do not know if many sites nearer the river than the Wilcox Ranch and if that's the case, I think it would be really difficult logistically to make a worthwhile trip to see the archaeology in Range Creek via the river unless you coordinated something with the University of Utah caretaker at the Wilcox Ranch or a permitted tour company.
To add....you are not likely to find written material on specific site locations for the canyon. There is a fairly explicit ethic that ruins of this caliber remain a "show and tell" style only. It has taken years for friends of mine who are archaeologist to even get invited to the canyon with professionals.
There are a ton of ruins and art throughout the main river canyon if you have an understanding of the basic principles. Most of the canyon remains unpublished but you can find more than expected with a little exploration (at least from putin to Range).
Take an extra layover and explore. We have always found something new, either ruins or fossils.
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