June Cat trips tend to be difficult to plan because the potential of high water means your camp choices are limited. So, you'll be racing all the commercials and any other privates for only a few spots (and Brown Betty is a prime target).
If your plan is to go during the summer, consider pushing your trip back a month to mid July. You should still have nice water, but more choice of camps and better access to hikes. There are tons of wonderful camps in Meander Canyon (the stretch between Potash and the Confluence). To see some historical markers, stop above rapid 15 and hike down the scout trail on the right to the rocks near the river. Kolb camp (between BD2 and BD3) is named for an engraving on the wall.
If you have a motor, timing should not be an issue. Feel free to shoot me a PM
Have a great time!