I've also seen it mentioned that shoulders can be better on the southbound side; don't know if that's true. Maybe because of the large number of cyclists, drivers won't be surprised to see you on the highway. I'm not sure what the car-vs-cyclist collision rate is there versus other parts of the country. What I hate to read about is a cross-country cyclist getting hit by a pickup on a lonely Texas road with no other cars for ten miles.

The state and perhaps a few county parks are going to be your best bet for hike and bike sites with hot showers. I've seen reports about the KOA near Manchester State Beach giving cyclists discount rates with better amenities than the public campground.