Suppose once this case is decided a case challenging Article II eligibility is brought by some other party.
Eligibility is determined by three factors:
Clearly the person is ineligible, therefor they "shall not be eligible to the Office of President". They can not be President. Article II does not say "shall not be a candidate for the Office of President", they "shall not be" President.
There is no restriction on the Judiciary to try the case, indeed they must.
When a person is removed - for any reason: death, disability (25th Amend.), impeachment, resignation, or ineligibility - a vacancy is created in the office, the succession process applies.
I do understand your argument. I just disagree with it.
I believe a court under those circumstances would explain to the parties that the Constitution commits to Electors the function of choosing a President and that their argument should be directed to the Electors and to the voters who elect the Electors. I think that it would be a very simple case. Just read the Constitution to find out who chooses presidents.
I recognize that there are people who believe that there exists some fundamental problem with any system that entrusts to someone other than a judge a final determination of an important issue. But, I think most judges would have no difficulty with that notion.
Obviously, you and I cannot resolve this question. Maybe someday soon someone will somehow force a judge to decide whether he thinks he has the powers you are claiming for him. I predict that he or she will look for a way to avoid even answering the question and if he or she is somehow forced to answer the question, I am almost certain that he or she will find a way to decline to disqualify any candidate for president.