Lloyd said:
The CI model I think assumes that electrons get squeezed out of the ions, that degrees of freedom are lost and heat or something converts to electrostatic potential within the positive double layer.

That's correct. When the spacing between the atomic nuclei is too small to allow electron shells, the electrons are liberated. Then, by the Pauli Exclusion Principle, they are expelled, leaving positive ions behind. The electrons congregate in the nearest space where there is room for them. In the case of the Sun, this is to the outside, where the compression relaxes because of the diminishing gravity. The electric force, as repulsion between like charges within their own layers, and as attraction between opposite charges across the layers, removes degrees of freedom, reducing the hydrostatic pressure. Thus it could be said that hydrostatic pressure (i.e., thermal potential) has been converted to electrostatic potential.