@SansaSnark I agree. So the question now becomes, rather than "How can we get our children back to school as quickly as possible?", "How can we determine the extent of transmission in schools?"
I would think that the cheapest and easiest solution to this is "Wait a month and see what happens in the rest of Europe"
Given that many places have both better testing and lower case numbers than we do, do we not think that these other countries are better placed to find this data with less risk?
So far, Denmark have stated that returning some primary school children raised R by 0.3. Sweden believe there is little effect. Germany and France are just returning their students over the next week or so. Since we are a couple of weeks behind, why don't we wait and see?
If there is no rise in transmission, then we do not have to worry about rotas, etc for students and can focus exclusively on preventing adults from mixing.
If there is a rise, but only for students above a certain age, then we can look at focusing on home learning for this age group.
If there is a rise, but it is moderate, we can look at part time schooling and distancing measures.
If there is a large rise, then we need to realise that schools will not be able to open enough to provide either much education or much childcare, and we should look at school provision as providing a role in mental health and safeguarding work primarily and focus on this aspect.
Until we know more about transmission rates, deciding how we want schools to look is pointless.