Here in The Netherlands we solved this problem. We have a system of public schools (which are owned by the government) and "special" schools (which are based on religion or life philosophy). In the historical "School Struggle" it was decided that the government had to fund the special schools equal to the public schools. This results in a weird situation where special schools get both money from the government and from tuition fees. As a result, those schools have better results.
I find it strange that your government refuses to help these schools. In my opinion the education of children is most important, everything else doesn't really matter.