There's a nice camping area at Potholes, several miles up Escalante Canyon. It has shade, a picnic table and vault toilet.
If it is still running high, you'll make good time on the river. The Whitewater take-out only has room for one boat at a time, and it can be tough to hit it when the river is this fast. You'll need to be on your game. Be sure to have a good look at it when you run shuttle.
There is at least one shuttle service permitted through BLM for that section if you are concerned about break-ins at Whitewater. Info here