Thanks for taking the time – very interesting! I see the key is the idea of a field; I do vaguely remember that result for electric fields inside a hollow sphere from Physics many moons ago. It seems my intuitive idea of 2 hemispheres close together, & moving slightly off-centre making a big difference, is misleading.

So perhaps there really is a race of super-intelligent (heat- & pressure-resistant) beings at the centre of the Earth after all.. :)