So, my advice is to take a pair of dry boots and a pair of water shoes. My assumption is that when you're in the water, you're in the water or close to it for several hours. And when it's dry, it'll be dry for a while. So you shouldn't have to swap shoes 20 times a day. Plus, most aqua shoes are so light that carrying a pair isn't a huge burden. For example: Teva's Gamma ($60; www.teva.com), an aquatic shoe that provides full coverage to your feet but still drains fast. Very grippy soles give traction on wet and submerged rocks. Better still, weight is only one pound, eight ounces per pair. The Adidas Hellbender ($90; www.adidas.com) is slightly heavier, but also a little beefier, which may be better for you on rough river bottoms. And they'll manage the in-between sections a little better.
As for your dry boot, any good mid-weight backpacking boot should work well. Lots of people really like the Asolo FSN 95 ($150; www.asolo.com), a light but capable shoe that has a Gore-Tex bootie should you want to indulge in some puddle-splashing. The same goes for Montrail's Torre GTX (also $150; www.montrail.com). If you're carrying a really large load (45-plus pounds) and will be on very rough terrain, then move up a notch with a boot such as the Lowa Trekker ($200; www.lowaboots.com).
Sounds like a fun trip!