Welcome to Free Republic.
You seem well-versed, I am curious as to your view of whether the 20th A. refers to a duty of a President elect to “qualify”; and, if so, what the ratifiers may have had in mind.
If there is a duty, what is your view with regard to whether such a Constitutional duty is one a Congress can routinely dismiss? (Of course, 3 USC 15 appears to give the Congress the authority, if not the obligation, to object to any substantial election irregularities.)
If there is a duty, do you believe it is one that expires if an ineligible candidate is given the office?
The language that says "If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified" is meant to deal with the situation where the EC has not confirmed the President before his term starts. In that case, the VP would serve as President until the EC (or Congress) picks a President. When the EC cast their vote, Barrack Obama qualified as President for purposes of this Amendment. This sentence seems to deal with a situation where, for whatever reason, the EC is unable or unwilling to vote in the President and/or VP. It's meant to prevent the existence of a power vacuum while the mess is sorted out.
If, down the road, it is determined that Barrack Obama was not a NBC, then the VP becomes President, just as if the President died, was incapacitated, resigned or was removed via impeachment.
I realized that I didn’t answer your question regarding a candidate’s duty to qualify.
The 20th Amendment doesn’t deal with issues like NBC. When it talks about qualifying, it’s referring to a candidate getting qualified as President either by a vote of the EC or Congress (which votes if the EC can’t decide). After November 4, the President Elect doesn’t really have a duty to do anything, other than show up on Inauguration Day to be sworn in.