Why do the pennies in the pre/post 1982 penny experiment sometimes dissolve completely? USA pennies were nearly pure copper pre-1982.  Post 1982 they are copper clad zinc.  A common experiment in US high schools is to notch pennies with a file and add them to an HCl solution.  The old pennies remain untouched and the zinc of the new pennies dissolves, leaving the copper cladding.

Sometimes the copper cladding also dissolves and sometimes a considerable amount of the old penny dissolves.

Why does the copper dissolve?

I propose that the copper in the penny is reacting with atmospheric oxygen, forming copper oxide that dissolves in the acidic solution.

Another proposal is that the formation of a complex ion between copper and chloride ion drives the equilibrium, allowing the copper to react in HCl.  This is analogous to how aqua regia dissolves gold.

Another proposal is that the copper oxide layer on the penny reacts with copper metal in a comproportionation to form copper (I) ion that then reacts with oxygen to make copper (II) and dissolves?

Which is right?  Why does the copper dissolve?
Your conclusion about formation of the Copper Oxide is correct, but not about the reaction with atmospheric oxygen.

The origin of the Oxygen is from the hydrochloric acid solution. The solution does not mean is pure HCl , it means is a dissolve in water.  There is a redox reaction with water

I leave to you to find the redox reaction.