Since ZBaird's on the Omo I'll field this one.
It'll be a long day but you should be able to make it if you get a very early start from Black Rocks. I think its about 4 hours rowing to the ranger station without a motor but may be wrong. Make sure to have your act together when you get to the ranger station and you should be able to get checked through pretty quickly. Just be ready to show them all the required gear.
If you don't have any compelling reason to camp below the rapids, you may want to reconsider and camp at one of the upstream campsites. Consider having to deal with an emergency on the river as the sun is going down, especially when the temperature's dropping into the 40s or 30s. Also, that late in the day at this time of year, you probably won't have much, if any, direct sunlight in the Canyon, especially as you're running the rapids. Then consider that the first campsite below the rapids, Big Hole I think, will be a big mud hole after the high water last weekend. These things given, Miner's Camp or Upper Couger Bar should be starting to look pretty good....
There are just too many good hits to be shivering and tired when you get to the rapids.
Flow's forecast for about 4500 which is perfect for splashy fun, the water's going to be pretty cold though.
PS - in a loaded 16' cat you should be able to punch Sock-it-to-Me.