'Nannies are expensive and only an option for the well-off'
You can save money with a nanny share. Or just use one for some hours so your DC are not alone the whole time. It is something of a luxury option though, certainly.
'au-pairs only an option if you have extra space for them to live- so again, an option for the well-off'
A full-time au pair certainly, but you will find in the summer au pairs are available for short term contracts as their normal family goes away/sees grandparents etc. and they look to make extra cash. This is only option of you live in an area with lots of au pairs though obviously!
'students are not available in the day and tend to go him in the summer'
They are available in the daytime during the school holidays. The fact that they're home is exactly the point. They're home and looking for work just for the school holidays, that's why they're such a good option.
'not sure what age babysitter you would want to supervise an 11yo all day or that anyone would want that job.'
I think anywhere from 17 up, depending on maturity levels of everyone involved. I don't think it would need to be all day, an 11 year old can stay home for a few hours, it's just to break up the all day/every day problem. Lots and lots of students, au pairs and nannies look for short term work over the summer. I think looking after a teen is comparatively very easy so I imagine lots of people would be interested!