Actually, there is precedent. But the Constitution is clear on this. The sole purpose of impeachment is to remove a president, or other elected official, from office.since he's gone, they can't touch him.
I believe you are correct that a couple of judges or other officials have been impeached this way in our history. However, they were not the President. As you say, the Constitution is quite clear on this
Chief Justice Roberts will probably not want to have anything to do with the trial in the Senate. If he is smart he will avoid it like a plague by recusing himself from the trial because he and the court may yet have to hear cases related to this creating a conflict of interest for Roberts if he presides over the impeachment trial. There will be no trial.