What is the Difference between a Hydrogen Atom and a Neutron?

This is a follow up of the previous post on Real Quantum Mechanics applied to atomic kernels.

A Hydrogen atom is composed of a small positive proton kernel and a surrounding large negative electron charge density cloud held together by Coulombic attraction. The binding energy is 13.6 eV. 

A neutron decays into a proton and an electron (and an antineutrino) releasing 0.78 MeV based on the rest masses of the neutron, proton and electron. We can thus view a neutron to be composed of a proton and an electron with a binding energy of 0.78 MeV,  thus with the same components as a Hydrogen atom with a binding energy of 13.6 eV, with a scale factor of about $10^5$.

Thus the same components but vastly different energies, how come? The neutron must be composed in a different way from a Hydrogen atom. The only possibility is to switch the roles between proton and electron and view a neutron to be composed of a very small electron kernel surrounded by a small proton cloud. 

A Hydrogen atom and a neutron will then be described by the same Schrödinger equation, with only a change of spatial scale with some factor $S$, and then with ground state energies also scaling with $S$.  

With an energy scale factor of $S=10^5$, we would thus expect a neutron to be about $10^5$ times smaller than a Hydrogen atom, which is confirmed by observation. 

We thus find experimental support to an idea of viewing a neutron to be composed of a very small electron kernel surrounded by a small proton cloud as an explanation of its very large binding energy compared to a Hydrogen atom. 

Nucleosynthesis into heavier elements would then start by transformation of Hydrogen=proton+electron into neutron=electron+proton under very high pressure and temperature, followed by proton+neutron synthesis. Synthesis of proton+proton into 2proton would then not be needed, and in fact is not observed. But electron+electron into 2electron seems to be needed.