Hi Neil,
I've ridden Koko twice in the Spring (late May), both times straight-through without camping. So, logistics are going to be pretty different for you guys than my 24-26 hour efforts--and I probably won't be able to help you as much as I hoped. But here's whatever I can think of that might be helpful.
In the Spring, riding from Moab to GJ, I have gotten water at:
1. The junction of Mountain Loop Rd and Castleton Rd. Small creek on the right side of the road. Not sure if it's running in the Fall. If there's snow up high, it might be good.
2. Fischer Creek before dropping down into the valley. Lots of water in the Spring, and I assume that there will be some in the fall if there's been snow up high.
3. Hideout Campground. Very small spring that crosses the trail. I don't know if it flows in the Fall, as it's already pretty slow even in the Spring.
4. Westwater Ranger Station. There's a spigot by the maintenance shed. Not sure if they turn it off when temperatures dip though, since the pipe would probably freeze.
I've never done it, but you can also get water from Salt Creek after Rabbit Valley. Murky and full of run-off junk from the fields above. Probably not a whole lot worse than the Colorado River though. A pre-filter that deals with silt if you are pumping would be helpful for the Colorado River and Salt Creek.
If you're going self-supported, I think that water will be a challenge this time of year. Might be worth doing some water drops in places that aren't near the river, such as in the La Sals and near Rabbit Valley.
It's going to be COLD out there, and likely wet/snowy/muddy in the La Sals. You probably already know this, but it's nearly impossible to ride long stretches of Kokopelli's if it's wet. There's a shortish section of trail between Sand Flats Road and Mountain Loop Road on the climb to the La Sals that is especially gloopy bentonite. If it's wet, you'll need to carry your bike for a couple of miles. Lower sections dry out more quickly though.
Good luck, and have fun. I'd love to hear how it goes for you! You're brave to be heading out so late in the year. Did I mention that it's going to be damn cold at night--especially up in the mountains!
