You could do a float trip on the Ouchita River. It's about as close as you can get for backpacking.

A "float trip" is not a "White Water" thing, it's a "floating" thing. You meander down the river and let the current do most of the work. Most of the outfitters have very high quality canoes they rent that are made for the type of water you'll use them on so they are stable, easy to maneuver, and comfortable.

I use all the same gear I use when backpacking. I don't take anything different, though I can take a few luxury items along because I'm not carrying them on my back all day. Having a chair at camp is pretty sweet and you can take one on a float trip.

The scenery is amazing, the places you can camp are amazing, and you can do short hikes to super scenic spots along the way, plus take a swim in wonderfully pristine water anytime you want to cool off.

The key to enjoying a float trip is stop along the way and explore. More miles does not equate to more fun. Stopping and checking out all the cool spots you'll be seeing does though. If you talk to the outfitters they'll tell where the best spots are to camp and hike how far you should plan on going to get the most out of your trip.

Weekdays are better because if the weather and water are good on a weekend the rivers will be filled with people enjoying themselves.