Earlier quoted context omitted.
What motivates your first factor? 0.782343 MeV is the free neutron beta decay; where in the solar system are the free neutrons minutes after they are magically teleported to terrestrial ground zero as a something like a (degenerate, possibly ultra-relativistic) Fermi gas? I think most attempts to arrive at an answer will end up somewhere between half and virtually all of them being "not very close" (~ light-minutes)…
> I think most attempts to arrive at an answer will end up somewhere between half and virtually all of them being "not very close" (~ light-minutes) away Mean free path of free neutrons moving past normal matter is only in the order of centimetres, exactly how many centimetres depends on the neutron energy and the specific nuclei it's interacting with, but still order of centimetres. Given the relative masses, I can…
We seem to agree that free neutrons don't stay free neutrons when they slam into the solid earth.
I too wanted to think about neutrons as a non-self-interacting gas, but that just doesn't work: Meyer 1994, https://ned.ipac.caltech.edu/level5/Sept01/Meyer/Meyer3.html (Paragraph beginning with, "Only the strong gravity of the neutron star keeps such matter from exploding apart." Cold in this context is partly explained in the preceding paragraph; in inner regions the matter is a degenerate gas meaning the particle kinetic energy becomes dependent on the density or equivalently pressure becomes independent of temperature; even at enormous pressures, degenerate gases don't hold much thermal energy -- that was practically all radiated away when the NS was young. Our teleporting (of inner region matter) therefore engages a very low-entropy r-process.
Outer regions are just too complicated and varied for a HN comment. The crust is thin -- a few to a few hundred metres or so compared to an NS radius of ~ 10km. It's also much less dense, so is a small fraction of the NS mass, and thus maybe not a target for our teleportation. Here's a 180-page open access review: https://link.springer.com/article/10.12942/lrr-2008-10 Pesky electrons and protons complicating things.