I will only address this part of the question:
Who would be able to authoritatively decide the constitutionality of such a question, with all Supreme Court justices having clear conflict of interest on the matter?
The Supreme Court could still hear such a case, as the justices make their own decisions about when to recuse themselves. In particular, they ...
Not at all
Well, except that a contempt of court charge would also apply.
The bailiff would make an arrest and transfer custody to the police who would follow their normal process. Witnesses would be interviewed and ultimately testify. The judge , as a witness would not be able to hear the case so it would be brought before another judge.
It's not uncommon. In fact I am aware of at least one case where the trial judge referred it to appeal before he made his decision on the basis that whichever way he decided the law was so unsettled that grounds for appeal would occur. In that case the court of appeal called up the trial judge to sit on the 3 judge appeal a) because he knew the case and ...