When the electrons and protons are converted into neutrons the neutrons are not degenerate.
Ok, that clarifies what you meant. I don't think it's correct, though. As I understand our current supernova model, or at least the one that's relevant for this discussion, gravity overwhelms pressure in the core of a star when nuclear fusion shuts down and the core's mass exceeds the Chandrasekhar limit. The star's core at that point is at white dwarf densities, not neutron star densities--i.e., the density is way too small to force inverse beta decay and convert electrons + protons into neutrons. It is true that the neutrons are not degenerate at that point; but that's irrelevant to the collapse process, because the collapse is not driven by the core radiating away excess heat from non-degenerate neutrons; it's driven by gravity overwhelming pressure. Electrons + protons turning into neutrons won't happen until the core has collapsed almost to neutron star densities--at which point the neutrons are degenerate.
In the thought experiment of Ken G the end product will be a degenerate proton gas
embedded in a see of electrons that are no longer subject to PEP due to the "magic wand".
No, it won't, because, by the same argument you gave for neutrons at white dwarf densities, the protons in the white dwarf just after the magic wand is waved are not degenerate.
Such a body could be similar to a neutron star.
No, it won't; see above. Nor will it collapse the way a supernova's core does, because the starting point was a stable white dwarf, which means its mass must have been below the Chandrasekhar limit, and therefore gravity does not overwhelm pressure. That means the key process going on in this case, unlike the core collapse supernova case, is heat transport.