Here's a partial answer. https://www.law.cornell.edu/uscode/text/10/253
Section 253 has two parts. The first allows the president to use the military in a state to suppress “any insurrection, domestic violence, unlawful combination, or conspiracy” that “so hinders the execution of the laws” that any portion of the state’s inhabitants are deprived of a constitutional right and state authorities are unable or unwilling to protect that right. Presidents Dwight D. Eisenhower and John F. Kennedy relied on this provision to deploy troops to desegregate schools in the South after the Supreme Court’s landmark decision in Brown v. Board of Education.
The second part of Section 253 permits the president to deploy troops to suppress “any insurrection, domestic violence, unlawful combination, or conspiracy” in a state that “opposes or obstructs the execution of the laws of the United States or impedes the course of justice under those laws.” This provision is so bafflingly broad that it cannot possibly mean what it says, or else it authorizes the president to use the military against any two people conspiring to break federal law.
[Given the states lack of ability or lack of will to enforce the election laws, in my opinion, fits within this statute of the Insurrection act. Is that Treason?. In this reading, it would read as conspiracy.]
Is that conspiracy to commit Treason?
could be if you link it to this
https://www.law.cornell.edu/uscode/text/18/2385 18 U.S. Code § 2385 - Advocating overthrow of Government Whoever knowingly or willfully advocates, abets, advises, or teaches the duty, necessity, desirability, or propriety of overthrowing or destroying the government of the United States or the government of any State, Territory, District or Possession thereof, or the government of any political subdivision therein, by force or violence, or by the assassination of any officer of any such government; or
Whoever, with intent to cause the overthrow or destruction of any such government, prints, publishes, edits, issues, circulates, sells, distributes, or publicly displays any written or printed matter advocating, advising, or teaching the duty, necessity, desirability, or propriety of overthrowing or destroying any government in the United States by force or violence, or attempts to do so; or
A bigger question would be how these two fit within the 'emergency declaration' clauses and how the upends civilian law. Does that cause some technical leeway into use of "Continuity of Government"? Lots of stuff in there that is 'classified' to civilians that might be able to be used depending upon how it is written.
Also one more thought.
If an emergency declaration could be construed under the same legal framework as the US Civil war, then the trial of Mary Surrat looks like a framework that could be used. that was UCMJ and she was convicted of 'conspiracy'. Judge Advocate John Bingham presented the closing argument for the prosecution.[166] The military tribunal had jurisdiction, he said, not only because the court itself had ruled at the beginning of the trials that it did but because they were crimes committed in a military zone, during a time of war, and against high government officials in carrying out treasonous activities.