“the Constitution reserves to Congress the right to over-ride such a veto and to remove the President”
Impeachment is subject to Amendment VIII with respect to due process.
The Supreme Court could have the final say.
Amendment VIII has nothing to do with due process; surely you’re not saying that impeachment is cruel or unusual beyond the unusualness of the crime?
As for due process, impeachment IS the Constitutionally prescribed due process... although certainly if the President challenged the impeachment on any grounds, the Supreme Court would be obliged to consider those grounds. But I expect on consideration, it would defer to the Congress to make any legal decision beyond deferring to Congress.