This is a pedantic argument from them. Yes, technically, the constitution mentions march 4th and the 20th amendment mentions the 20th of january.
The suggestion here is that you would throw out the the entirety of the US Code - but you'd still be up a creek.
The constitution Article II Section I specifies the use of electors to nominate the president. It also states "The Congress may determine the Time of chusing the Electors, and the Day on which they shall give their Votes; which Day shall be the same throughout the United States." Which means that the constitution endorses the use of the US Code.
Hahahah. Conclusive means pending? The controversy as regards the nomination of the electors is not that someone alleges controversy, or else literally every sore loser in history could have bogged it down with frivalous lawsuits that go nowhere.
But alright, mix-up of terms. See, the contingent election triggers if a candidate doesn't hit the absolute majority of electoral votes. I thought the suggestion was that the Congress would just unilaterally reject the vote, which seems unrealistic to me. So yes, if you can get conclusive controversy down by tonight and somehow flag enough votes that there is no majority in the college, you can trigger the ol' 12th amendment.
As regards the consitutionality, sure, as above. It's a technicality. As regards prima facie, it appears that there haven't been much success in the courts in doing that - a lot of those affidavits have been given to committees that deem them unreliable, and a lot of the video evidence seems to be getting rebutted by affidavits from election officials, like that atlanta state farm arena thing. You could try to lodge a court case in the same way, but thusfar it doesn't at all appear to be prima facie to anyone with authority in government. Indeed, it appears to be "claim - rebuttal - actually that rebuttal is totally false and while I can't make a specific statement just look at this footage right here does that not look right - rebuttal - you're a democrat plant".
But, yeah, prove me wrong. Lodge something tonight that disputes the electoral vote. Or don't, and then try again to dispute it and drag that case to the SCOTUS to argue the merits of Safe Harbor.