First, like you very astutely pointed out, stop making school mandatory. Even encourage families to keep kids home if they have childcare available. That probably entails ceasing any academics, since parents will otherwise feel pressured to keep their kids in school lest they fall behind.

Second, we can keep kids isolated in small groups, so they're not intermingling as is typical during a school day. A child should be assigned to a single pod, and only interact with his assigned pod for the remainder of the epidemic. Obviously childcare workers should be assigned a single pod, and stay in that pod. The smaller we can sub-divide pods, the better.

Finally big common activities, like lunch or recess should be staggered so that kids aren't ever exposed to anyone else outside their pods. Other than that pods should stay confined to the same classroom for the duration of the epidemic. Pods should probably be assigned based on busing routes, so that kids only bus with their pod.

Here's a problem: what's the difference between state-provided daycare and school, from an infectious disease standpoint?

Both are a bunch of kids in one building, attended to by adults. Both will require busing kids to said building, with buses driven by adults.

Might as well just leave the schools open.

I don't have a solution, just pointing out that daycare == school for this situation, so closing schools but providing daycare in it's stead won't make a difference.