Nothing here says that one party gets to define anything. Also, the court did not say that the Senate must agree by a 2/3 majority, only that Congress must decide. The text of the constitution does clearly make section 3 self executing but, unhelpfully, it does not tell us who determines that an insurrection occurred or whether a particular person is guilty of participation.
It clouds the issue even further that the previous vote failed in the Senate, but would have passed by a simple majority. It could well be that some who voted in favor of impeachment might have voted otherwise if a simple majority were required. I think a simple majority should be sufficient in this case, but that vote never occurred.
Personally, I'm not sure it would be a good thing to remove Trump from the ballot. I think it will be far better for the nation to defeat him at the ballot box. If Trump can actually win, then we are doomed anyways.
Trump is uniquely bad as a human being, but he is not uniquely bad as a potential Republican president. There are plenty of Republicans that would be worse, simply because they are competent and, for many milquetoast Americans, far more persuasive.