No question of bending the rules here, Steve. The matter of determining whether an impeachment process can be concluded after the person who has been impeached has left office is a purely constitutional matter, which should have nothing to do with the Senate. It's quite distinct from the task of whether the impeachment should be conformed or not, which is purely a matter for the Senate, and has nothing to do with the Supreme Court. And, as you say, no punishment is involved. That is what criminal courts are for.

Interestingly, so far as I am aware, there is no mechanism for dealing with the problem if the Supreme Court does act improperly or even unconstitutionally. (I think if it declined to rule on the constitutionality of impeaching a dead parrot, so to speak, I think it would be failing in its duty.)

But for the Senate to decide a constitutional matter like this strikes me as a clear breach of the principle of the separation of powers.