I would call the Moab BLM and verify your options. From the online resources it appears you are likely only allowed to camp on islands in that stretch and even that may be off limits.. According to this BLM page all land on either side of the river at least to Gold Hole is off limits to anything other than designated campsites:
Moab Dispersed Camping
The list of approved campgrounds can be found in the link below. Sadly, they are all firs come, first served but there are a ton of them:
The river page states
Special regulations apply for river runners wishing to camp along this section of the river. On river left (to the left as you are facing downstream), camping is allowed only at BLM Utah, Moab Field Office Campgrounds. River runners may camp at designated sites on river right (to the right as you are facing downstream) only between Dewey Bridge and Salt Wash (the boundary of Arches National Park).
Moab BLM really started cracking down in the mid-aughts and designating dispersed camping to very limited locations. And I have seem them ticket people who try to stealth camp anywhere near roads or trailheads. Considering you will be there during a busy season I would advise caution about camping in any undesignated location, including sleeping on your boat.
Best of luck on a what sounds like a great trip.