My family did not have to pay anything for me to attend because the Gülen school was a charter school (funded by tax credits). The problem with an officially Muslim school though would be that religious schools are not allowed to be charter schools.
That being said, the Gülen school was able to get charter funding in spite of odd behavior on their part. For example, even though there were very few Turks in the city I lived in, 50+% of the teachers at the school were Turkish. They would bring them over on H1B visas, even though I can't think of a justification they would give for bringing in so many teachers specifically from Turkey. But they do it and it touches a bit on this in the video.
The result of having so many Turks was a strong Turkish cultural influence on the school. Students had a positive opinion of Turkey, and many would take class trips to Turkey. Maybe you could start a school and import teachers from a part of the world that has many good Muslims.