Mostly followed Southern Tier routes until LA or so where I switched a bit more to following US 90 closer to the coast. I've also made a few other trips through parts of the south. I made my Southern Tier trip in March/April and that was a good time of year.
These are overly broad generalizations, but I tend to find more shoulders in West of US than East and in North of US than in South. So I've been on a few US highways (US 67 in MS coming into Memphis comes to mind), with high speed traffic and not much in way of shoulders. I also had an instance where road construction on I-10 diverted a lot of truck traffic onto nearby US-90. With those issues aside, I found the smaller roads in LA, MS, AL and TX and the choices made by Adventure Cycling routes to be reasonable.