I consider the Senate impeachment trial to be a serious undertaking, and while different than a state civil trial there are some similarities in evidence presentation and arguments.

It is a serious undertaking - but it is not a judicial undertaking. It is thus wholly dissimilar from a state civil trial. The impeached individual has no due process rights in those proceedings - they have no right to present evidence, call witnesses, cross examine witnesses, or even provide argument. Historically, the Senate has chosen to provide some very limited procedural rights to the accused - but it's not anything like a civil trial. For the January 6th impeachment, the Senate chose not to have any witnesses at all - so neither the impeachment managers nor Trump were allowed to have witnesses (or cross-examine the others').

The OP 126 page law review article says "in principle: Section Three's disqualification rule may and must be followed, applied, honored, obeyed, enforced, carried out by anyone whose job it is to figure out whether someone is legally qualified to office, just as with any of the Constitution's other qualifications". Whatever the Secretary of State decides, a civil lawsuit will follow, and the issue will be decided in a state court, with all of the normal appeals all the way to the Supreme Court.

Yeah, that's just wrong. I work with local government staff and employees all the time (though not dealing with elections - my specialty is zoning). Universally, their job is not to interpret the U.S. Constitution. If you want to argue that some law, some decision, or some action violates the Constitution, you're welcome to go to court and get a court to tell them that there's some rule they have to follow that isn't in the ordinances or state statutes they're obligated to apply. Unless you do that, they have to follow the black letter of the law. They only get to make the decisions that state election law empowers them to make. Unless the state election law gives them the power to make the call whether someone is a rebel or insurrectionist, then it's not their choice.