I've paddled from Ha Ha Tonka upriver to the Onyx Cave, and all around Lake Niangua, but was never brave enough to make the full run downriver from the Tunnel Dam to the Lake of the Ozarks. One of the first things you see below the Tunnel Dam is low water bridge (Whistler?) that is impossible to navigate by water, and not knowing just how many of these there are my concern was that the run would require several portages. Thankfully that doesn't seem to be the case and kayakers and canoeists travel is now authorized (but you do need to put in below said bridge).
The Missouri Master Naturalist website created an annotated google map of the area so you know what you're getting into, but it looks like a great way to spend the day on the kayak. I'm looking forward to making the run myself as soon as I can and will post some pictures.