I suppose they could get some insurance company to offer a policy that costs them extra money just so their employees don't get free birth control.

That's exactly what Hobby Lobby did. Then they don't pay enough for employees to buy their own birth control and the employees have quiverful families just as God has Ordained.

You simply can't use reason or logic with these folks, they're Christians.

And I beg to differ about private schools which have private funding as well as federal funding, smaller enrollments, larger classrooms, and parents with health insurance and jobs. They'll nail the distancing and hygiene and have far fewer cases and deaths than the schools where poors are sent.
Good coffee, good weed, and time on my hands...