I do not have faith in Congress ever addressing this issue as their negligence to uphold their oath to the Constitution is as traitorous as the usurpation itself. The States need to pass one simple law and this would never happen again.
I call it the "Usurpation Protection Law". It would require documentation from Congress and the President proving that the Twentieth Amendment, section three was complied with and that eligibility was no longer an issue BEFORE the State would recognize the legality of the president. Any failure to prove compliance would then automatically trigger an investigation request from that State's representatives in Congress. This would certainly pass Constitutional muster in that it supports the enforcement of a portion of the Constitution itself. This law could be passed tomorrow and have immediate effect. There is no time limit on enforcement of the Twentieth Amendment, section three.
Who could reasonably oppose such a law? Certainly not a "legal" President.
As you correctly point out, that is what SHOULD happen.
More to the point, that is exactly what should happen in the short term...the Federal government isn’t going to do it, but the states could pass laws to keep people like Obama from getting on the ballot, which should have been done in the first place. If some of those big electoral college states do it, that would fix it right there.