Interesting; I'd seen this before but forgotten about it.
Don't think it works here though - if the pressure of reflected sunlight is counteracting gravity, then I don't see how the statite can be acting as a sunshade. If it were in position for that, the sunlight would be pushing it toward the Earth, no?
If anything this sounds more like the reflectors often proposed for Martian terraforming, which are designed to heat the planet rather than cool it.
A very different mode of Statite system operation is possible that would allow the Statite to be placed at any point around the Earth, at all times of the year, even over the sunlit side, at the expense of slightly greater operating distance. Instead of the Statite being balanced by sunlight in the gravitational field of the Earth, the Statite would be placed in orbit around the Sun, at such a distance from the earth that the gravitational field of the Earth plus the moon is only a perturbation on the gravitational field of the Sun. [1]
But in practice, I think you're right. Forward wrote a short story about such a "pole sitter" ("Race to the Pole"), and had one of the characters say this:
The control problem of keeping the [statite] balanced over the pole is very tricky, especially during the summer season of that hemisphere when the polar axis is over on the sunlit side of the Earth. That’s why ‘pole-sitters’ have to be placed so far away from the Earth. If they get any closer than 250 Earth radii, they become unstable during the summer. [2]
Don't think it works here though - if the pressure of reflected sunlight is counteracting gravity, then I don't see how the statite can be acting as a sunshade. If it were in position for that, the sunlight would be pushing it toward the Earth, no?
If anything this sounds more like the reflectors often proposed for Martian terraforming, which are designed to heat the planet rather than cool it.