I believe this has beend discussed on FR in the recent past. Speaker isn’t required to be a member of Congress.
The real problem is that impeachment of P&VP can’t be done simultaneously.
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.
The real problem if they tried that impeachment stunt would be the backlash they’d get from the American people.