I am thinking that a weekend down at Missoula on the Lochsa would be great. The weekend of the 23rd would work great. I believe it is a 6h drive to Missoula, and another 1.5h to the Lochsa. The hot springs would make a nice stop.
The Lochsa is a larger river, similar in size to the Middle Fork of the Flathead. Runs are class 3 and easy 4. There is also a beautiful surf wave next to the road when the water is high.
I would think leaving after work on Friday as soon as possible. Kayak all Sat, and Sunday morning and leave around 1:00 in the afternoon.