You may want to check into charter schools in the Denton area. I'm not sure if charter schools are common where you live at this time, but there are quite a few options in Texas. You don't pay anything to attend, just like public school, but they are privately run and sometimes have a specific focus such as math/science. They are accredited through the state.
I have never lived in Denton, but I know we really enjoyed our experience with Vista Academy in Carrollton. The school was smaller than a public school and all of the teachers pretty much knew all of the kids. It was a pretty strict environment also. Vista operates under the umbrella of Responsive Education Solutions. I know they have facilities in Hickory Creek and Lewisville, but not sure if either would work for you since they might be too far from where you want to live.
You definitely would want to get some referrals if you choose this route because the reputation of charter schools can really vary! You can also check their ratings through the Texas Education Association.