I agree with you on both of your major points, but would point out that a writ of mandamus is a very specific form of action:
Overall, an enjoining action is the only clear solution, but it would to find its force from more general principles rather than specific statutory authority, which makes gaining standing (and winning) more difficult in pratice.
@Saint Cad. Why would you have to do the whole 10 days dance? Just violate a law that was signed into law by Obama, and then say that the law is invalid because Obama can’t be President because he was born in Kenya?
Read Article I Section 7. If I claim that Obama is not the President then by default Biden is President. If a bill is passed and not signed by the President (Biden) within ten days excluding Sundays then it becomes a law. Biden has never signed a bill into law for obvious reasons - HOWEVER any bill passed within ten days of adjournment that does not get signed does NOT become a law because of the pocket veto.
Therefore even if Obama admits tomorrow that he was born in Kenya and SCOTUS rules in Biden v. Obama that Biden has been President retroactive to January 20, 2009 then almost every law Obama signed is still a law simply because Biden never signed them. The only exceptions? The bills passed less than 10 days before adjournment and NONE of those are laws.