Sorry to pop in late on this months-old discussion, but I wanted to share a few things based on my own knowledge as a resident of the area.
Samanthy mentioned "northwest of Green River", so the better-known Robbers Roost Canyon, closer to Hanksville, doesn't fit the description. It's located 45 miles south of Green River. I think Nugget Dog is hitting a little closer with his description near Buckhorn Wash. I'll hit on this southern location in a bit.
Page 111 of Some Dreams Die mentions Desert Lake. This area is certainly NW of Green River. I've never heard of it called the new-found Robbers Roost, but nonetheless, was apparently frequented by Butch and the gang during their time. Very little remains of Desert Lake. There isn't much more than a cemetery. However, very near there on Cedar Mountain, just a few miles east, is a hideout said to have been used by Butch. It can be difficult to get to, but I can tell you, it is a perfect place for a hideout. Getting there is like walking through a maze with 30 ft high walls. The easiest way down the cliff is by climbing down a dead Ponderosa tree leaning against it. The only remains of the hideout are some very old lumber scattered around a deep crack in the rock. The old timers tell the story of Butch using this crack as his fireplace. The smoke would rise through the crack and come out far from where he was located.
Also near this area, is Buckhorn Wash (Buckhorn Draw on the maps). Matt Warner, an outlaw who ran with Butch, etched his name on the sandstone there. It's still there and easily visible from the road. I've found other evidence of Butch in the area as well. The name "Butch Casady" is inscribed with what appears to be fire coals in sandstone under a rock overhang. Completely untouched by most of the elements, this inscription is still visible. The charcoal has protected the underlying sandstone from erosion leaving the inscription raised by about a quarter inch, possibly lending authenticity to the amount time it has been there. Also, since Butch's name was actually Robert Parker, it makes sense he might misspell it.
Now, back to Robbers Roost Canyon - It's been well documented that Butch and many others spent time there. Most notably in Pearl Baker's books. There is a chimney still standing from an old cabin built in the 1890's or so. As far as I've been able to discern, Butch may have never stayed in the cabin. It's said to have belonged to Jack Cottrell, a cattle rancher.
I can't imagine any of the outlaws would hide their loot in the canyon since there seemed to be fair amount of traffic through there in those days. Highly improbable of finding the hidden cache of bank robbery loot. However, there are many stories of shootouts there, so I think it's highly probable to find some shell casings, lead bullets or other relics.
We're planning a trip back in spring of 2021. We'll be taking metal detectors. Hopefully, I find more than nails.
Happy hunting.
Hammer