There are a few "values based" charters I think though, which might do the trick for you. I think the former catholic schools, now charter, would be a good place to start and I think there are a few others that have a specific values curriculum that they use.

1st Amendment aside, it would violate the spirit and the letter of DC charter law.

Perhaps OP is confused by seeing the applications by Hebrew and Arabic LANGUAGE programs with Jewish or Muslim religious schools.

If you absolutely want a Christian education, join a homeschool group or apply for voucher to a private school.

would violate the establishment clause of the 1st amendment

That's true, but they are no longer affiliated with the Catholic Church and had to change their curriculum to be non-religious.

The Center City consortium of charter schools were catholic schools that were converted to public when the Archdiocese couldn't afford to run them.

Charter schools are public schools and therefore cannot be religiously affiliated.

Do you know if there are any elementary Christian Charter Schools?