Remember the Chief Justice presides over the trial. Anything Mitch tries to do better happen before a trial is convened, such as (a) not bringing it up, (b) taking a vote on dismissal due to lack of Due Process and other civil liberties in the other Chamber, (c) etc. This could obviate the need for a trial and keep Roberts on the sidelines. I doubt if Roberts would press the point, although Schmuckie Schumer would raise all kinds of hell (to no avail).
Unfortunately rRoberts is another one we cant trust.