If your primary concern is finding a place to camp, you should not have a problem. The overwhelming majority of boaters are out for the day. If it were my trip, I would start looking for a good spot around 4:00 pm and settle for the next available spot once it hits 5:00 pm.
But it will be crowded. Upper end will be canoes and kayaks. I bet every permitted boat is out there and all the privates too. College kids will be out in force. I no longer enjoy such trips, so I would rather stay home. But then again, when I was in college at Mizzou, that's how I was introduced to Ozark float trips. So if the monster crowds only come out on certain weekends and leave the entire rest of the year for me, that is a more than fair tradeoff.
Where to go when it is crowded? Anywhere that does not rent boats is where I go. Scenery certainly sux compared to the Current. If I needed natural beauty as well, upper Jacks Fork would be the hike/float I would choose. Great scenery, great fishing, but it would be a lot of manual labor. Again, EVERYTHING easy and nice will be jam packed.