The real problem isn’t simultaneity, its that impeachment can’t be done at all—you need conviction by 2/3 in the Senate, and that isn’t going to happen. Fantasy on fantasy.
But, I didn’t know about the legal possibility of a non-Rep Speaker, unlikely as it would be.
Your confusing a House action with a Senate action.
Impeachment takes place in the House (the Grand Jury phase). Articles of Impeachment are passed to the Senate who hold trial and vote to acquit or convict.
Impeachment is only a stain on the legacy if Senate votes to acquit.
Re-read your #91 and realize it is your “confusion” but a simple erroneous statement of “can’t be done”. This conflates Impeachment with Conviction.
Impeachment CAN be done but conviction is highly unlikely, as you said. The “conviction” would be rendered as “Guilty of high crimes and misdemeanors.”