I understand why negative charge spreads out evenly across the outside of a sphere (as electrons repel each other), but I am having difficulty understanding why that would be the case with a positively charged sphere: That is to say, for the positive charge in a positively charged sphere to be spread out evenly across the surface, the few electrons around presumably need to be somewhere on the inside. But why would they flock to the inside if they repel each other, while positive charges are around both at the surface and further inside?
Imagine an electron exactly on the surface of the sphere. We assume the region outside the sphere is neutrally charged, so there are no electrostatic forces.
The sphere itself is positively charged, so there is an unbalanced attraction on the electron. It must experience a force that accelerates it into the sphere.
Yes, the other electrons are repelling each other, but there are not as many of them as there are protons. The electrons have to move (slightly) away from the surface for them to balance.
Net positive charge on the surface of the sphere would have its field projected outside of the sphere and have no effect on the electrons on the inside.
On the other hand, net positive charge inside the sphere would attract electrons surrounding it and make them move away from the surface, leaving the surface with the net positive charge.