I use US 281 to avoid Austin. Great 2 lane federal highway with some 4 lane divided sections from the Okla border to the Mexican border. A bit of local traffic near Marble Falls and crossing San Antonio.
US 67 is a good 2 lane with a few non-divided four lane stretches once past Dallas all the way to the Mexican border.
TX-16 is a good route. A bit hilly and curvy, but nothing to bother an RV driver.
Texas doesn’t have towns with stop lights every 10 miles like the east coast. Usually 20-40 miles between stop lights.
You’ve selected a good route. Not the fastest? But a good easy drive. You might want to pullover and let traffic pass you if several stack-up behind you. There are long sections without passing lanes.