Oh dear Gawd, you really don't want to go on Westwater at that time of year.
The flow's usually only about 3,500 cfs, you may get snowed on, it gets chilly at night, the water's getting too cold to swim in with the temperatures only getting up into the 70s during the day IF ITS EVEN SUNNY and not RAINING and/or SNOWING on you, you'll have to bring a bunch of cold-weather stuff just for night and even more in case the weather turns on you, you'll need a good stove to prepare hot meals and hot drinks, firewood is a real pain in the butt to lug on your rafts and you're going to need A LOT of it, (because...) it could SNOW that time of year, the days aren't very long, you have to change clothes, like, a zillion times because its cold in the morning, warm in the day, but it may get chilly if it gets cloudy, may get warm when the sun comes out again, then gets chilly when you go into the shade below Marble Canyon rapid after you get splashed and realize you need to dig out that splash top again, and then gets cold again at night, someone could fall in the cold water and get hypothermic, the possiblity of crappy weather combined with the shorter days really cuts your margin of safety in the event of a flip or swim, the rangers are burned out and starting to get irritable and probably won't give you a good campsite anyway, your friends (or girlfriend) that aren't as hardy as you will probably never talk to you again after you take them along for what they thought would be a fun-in-the-sun raft trip and they get SNOWED or RAINED on, lots of other people want to go at that time too for some reason I just can't understand so you might as well not even try calling in for a permit. There will probably be some really good football games whenever you want to go as well since teams will get into their conference schedules. Don't even bother, its just so much trouble, especially if you've never been in the fall - you really don't want to go...
Did I mention that you may get snowed on at that time of year?
That said, if you DO happen to get a permit, please shoot me a PM as I'd be glad to bring a 14' raft, blaster & propane, extra neoprene booties & gloves, wetsuits, spalsh gear, NRS Wing shelter, extra tarps, kitchen gear, and to help plan meals and bring anything else you need for the trip!