My first thought was heat, humidity and mosquitoes in S. La, especially if camping. I'd save that trip for late fall. And yeah, the flooding issue would be major I'd think relative to mossies. Missouri hasn't got a reputation for being a cycling paradise from TA folks, but would likely be cooler and less humid. If Oklahoma was a possibility, I'd recommend it for a mini tour. Done three tours there and really enjoyed them all. Lots of state parks, stuff to see and do, nice roads and nice folks in Oklahoma.
As we know, within reason, there is no really bad place to tour in the US in the summer if approached with the right attitude and preparation.