I live in Austin, TX, have St. Augustine grass, and since 2000 have mowed my grass with an old-fashioned reel mower.
I love it and want to encourage you to consider using a reel mower.
I have an Agri-Fab 18” Silent Reel Mower and it is excellent. Like most hand tools from a previous era, cheap mowers do not function well.
Like any hand tool, a reel mower requires a little technique. It’s not hard, but there are a couple of things to know.