Racers start at noon. To beat the racers you want to be past the flatwater and into the canyon before noon. Flatwater takes about an hour, so putting in at 11 would be the latest to be just ahead of the racers. Putting in at 10:30-10:45 would be a safer bet to stay ahead.
To put on in time, I'd look to be leaving pumphouse at around 10am or earlier. Bus shuttles seem to take a while to organize 20-30 boaters, so I'd be looking to start getting on a shuttle around 9:30 or earlier.
Put in road closes at 9am. If you absolutely need to get in there early, go for it, but there isn't a lot of room for cars with all of the activity for the race. I'd recommend parking at pumphouse, using the bus shuttles, and doing the race organizers a favor by using the shuttle logistics they have set up to help them make the event go smoothly.
Race info is on timberline's website
Colorado Premiere River Rafting: Gore Canyon Race 2010
Timberline is organizing the event, so they would be the folks in charge, with oversight by the BLM etc.