Doubling the concentration of extracellular calcium hyperpolarizes a neuron. Why?
This paper and this paper supports the second possibility I hypothesized. That is a increase in external Calcium concentration leads to an increase in conductance of Potassium. 

While the increasing the external Potassium concentration can be shown to depolarize the cell with by calculating the Nernst potential for the Ion, the Calcium Ion has a non-intuitive effect. This means if one increases the outside concentration of Calcium Ions then inevitably there will be a small increase in the internal concentration of Calcium ions on the inside. This will slightly bias the Calcium Activated Potassium Ions to be a little more open. Thus raising the conductance of Potassium. This will mean there is a net hyperpolarizing current keeping the cell less excitable.