Your exmples are “in theory”......hard to conceive that ever happening.
Please excuse the absurdity, the point I intended was that it's all up to whatever Congress decides is good enough. Grounds for impeachment is determined by the House vote, and grounds for removal upon impeachment are determined by the Senate vote. Congress decides what constitutes high crimes and misdemeanors as implied in the Constitution, and expresses that decision by voting.
So there's no requirement or justification for anything plausible, because sufficient enough votes gets it done.