Welcome to Texas. I have had a run of dog sprints this year. In years gone by if I had 2 a year it was a lot. This year I think I am up to a dozen or more. I live in northeast Houston and ride county roads like you. So far my defense has been speed but that is bound to not work sometime. (see my last ride at this link
Bicycling Texas | Bicycling, Texas | Cycling, Texas) There is a long thread about this subject on BF. The options and thoughts are many. My personal leaning is a electric cattle prod. The drawback is the closeness the dog must be to use it. A number of people carry pepper spray. Another option is a paintball gun. I am told the paintball stings and leave a mark but are not lethal.